Simplify the expression using the rules for
exponents.
Write your answer without negative exponents.
Answers
Step-by-step explanation:
(a×b^-3×c^-3)⁵ / (a^-3×b⁴×c⁴)^-5
let's look at the numerator (the top) first :
a⁵×b^-15×c^-15
and now the denominator (the bottom) :
a¹⁵×b^-20×c^-20
both divided are (due to the commutative rules of multiplication we can split this first into the parts of the individual variables, and then multiply them all with each other) :
a⁵/a¹⁵ = 1/a¹⁰
b^-15 / b^-20 = b^(-15 ‐ -20) = b⁵
c^-15 / c^-20 = c⁵
so we get as result :
b⁵c⁵/a¹⁰
Answer:
( b^5 c^5 ) / a^10
Step-by-step explanation:
Properties of exponent we are going to use:
First step: \(a^{-1}\) = \(\frac{1}{a}\)
Second step: \(a^{n} b^{n}\) = \((ab)^{n}\)
Third step: \(a^{m} a^{n}\) = \(a^{m+n}\)
Forth step: \(( a^{m} )^{n}\) = \(a^{mn}\)
~~~~~~~~~~~~~
1). \(\frac{( ab^{-3} c^{-3} ) ^{5} }{(a^{-3} b^{4} c^{4} ) ^{-5} }\) = \(( a b^{-3} c^{-3} ) ^{5} ( a^{-3} b^4 c^4 ) ^{5}\)
2). \(( aa^{-3} b^{-3} b^{4} c^{-3} c^{4} ) ^{5}\)
3). \(( a^{1-3} b^{-3+4} c^{-3+4} ) ^{5}\)
4). \(a^{-2*5} b^{5} c^{5}\)
\(a^{-10} b^{5} c^{5}\) = \(\frac{b^5 c^5 }{a^{10} }\)
Related Questions
What is the answer to 3/8 x 8/9 ?
Answers
Tell whether the given value is a solution of the inequality.
j+1>10; j = 9
A. Yes, j = 9 is a solution to the inequality.
B. No, j = 9 is not a solution to the inequality.
Answers
Answer:
Your answer is A
Step-by-step explanation:
Here you go mate
Step 1
j+1>10 Equation/Question
Step 2
j+1>10 Simplify
j+1>10
Step 3
j+1>10 add-1
j>9
answer
j>9
Hope this helps
Option B is correct, No, j = 9 is not a solution to the inequality j+1>10.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
We can substitute j = 9 into the inequality j + 1 > 10 and see if it is true or false.
j plus one greater than ten.
j + 1 > 10
We have to check whether j=9 is the solution of the given inequality.
Substitute j equal to 9 in the above inequality.
9 + 1 > 10
10 > 10
The inequality is not true when j = 9. Therefore, j = 9 is not a solution to the inequality.
Hence, Option B is correct, No, j = 9 is not a solution to the inequality j+1>10.
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HELP PLS ASAPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: C; 5.32
Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!
given f''(x)=4x-2 and f'(-1)=0 and f(-1)=4
find f'(x)=
find f(4)=
Answers
The inverse of the function
f(x)=(x+1)^2+2 if x ≥ 0 is
Answers
If \(f^{-1}(x)\) is the inverse of \(f(x)\), then
\(f\left(f^{-1}(x)\right) = x\)
We're given a domain for \(f(x)\) of \(x\ge0\), so \(f\left(f^{-1}(x)\right) = x\) is valid only for \(f^{-1}(x)\ge0\).
Now,
\(f\left(f^{-1}(x)\right) = \left(f^{-1}(x) + 1\right)^2 + 2 = x\)
Solve for the inverse :
\(\left(f^{-1}(x) + 1\right)^2 = x - 2 \\\\ \sqrt{\left(f^{-1}(x)+1\right)^2} = \sqrt{x-2} \\\\ \left|f^{-1}(x) + 1\right| = \sqrt{x-2}\)
Since \(f^{-1}(x)\ge0 \implies f^{-1}(x)+1 \ge0\), by definition of absolute value we have
\(\left|f^{-1}(x)+1\right| = f^{-1}(x) + 1\)
Then we end up with
\(f^{-1}(x) + 1 = \sqrt{x-2} \\\\ \boxed{f^{-1}(x) = \sqrt{x-2}-1}\)
. A cocoa blender makes a profit of 30% be selling a super mix cocoa at Kshs.650 for 250 grams tin. He makes a super mix cocoa by blending two varieties of cocoa., A and which cost him Kshs. 1 800 and Kshs.2 400 per kg respectively. B In what proportion the cocoa types A and B mixed? were (3 marks)
Answers
Answer:
The cost price of 250 grams of super mix cocoa is Kshs.650/1.3=Kshs.500.
The cost price of 1 kg of super mix cocoa is Kshs.500*4=Kshs.2000.
If x kg of cocoa A is mixed with (1-x) kg of cocoa B, then the cost price of the mixture is Kshs.1800x+Kshs.2400(1-x).
Therefore, Kshs.1800x+Kshs.2400(1-x)=Kshs.2000.
Solving for x, we get x=2/3.
Therefore, the cocoa types A and B are mixed in the proportion 2:1.
35 devide 28 with decimals pls help
Answers
Answer:
1.25
Step-by-step explanation:
The answer in decimal is 1.25
35/28= 1.25
= 35 ÷ 28
by 1
=35 - 28 = 7
Introducing decimals
= 70 to 28
by 2
= 70 - 56 = 14
adding zero to 14
= 140 to 28
by 5
= 140 - 140 =0
the answer is 1.25
I did it this way through division hope you'll understand. All the best.
Describe the graph of the solution set for g ≤ 13
Answers
I am grateful to anyone who can help. Thank you.
Answers
what is 32 divided by 616 please answer with step by step problem
Answers
Answer:
0.05194805194 rounded to the nearest tenth is 0.1
The vertices of triangle ABC are A (0,5), B (3,5), and C (2, 2). If the triangle is reflected acrossy-axis, then find the coordinates of the triangle ABC.
Answers
ANSWER:
\(\begin{gathered} A^{\prime}(0,5) \\ B^{\prime}(-3,5) \\ C^{\prime}(-2,2) \end{gathered}\)STEP-BY-STEP EXPLANATION:
We have the triangle ABC with the following vertices:
\(\begin{gathered} A(0,5) \\ B(3,5) \\ C(2,2) \end{gathered}\)The rule of reflection across the y-axis is the following:
\((x,y)\rightarrow(-x,y)\)We apply and we would be:
\(\begin{gathered} A(0,5)\rightarrow A^{\prime}(0,5) \\ B(3,5)\rightarrow B^{\prime}(-3,5) \\ C(2,2)\rightarrow C^{\prime}(-2,2) \end{gathered}\)what is the face value of the digit 5 in the number 48523 is
Answers
Answer:
500
Step-by-step explanation:
The value of 5 in the number 48523 is 500
hope that helped :)
what is the slope of the line that goes through the points (-3,8) and (0,23)?
Answers
Answer:
m=5 or the slope is 5
Step-by-step explanation:
This is because you use the expression y2-y1/x2-x1
Find the sum of 8, five times a number y and five times the same number y. Simplify the expression.
Answers
Let y represent the unknown number
sum of 8 can be symbolized: +8
five times a number y can be symbolized: 5y
and five times the same number y, symbolized: 5y
The expression is:
8+5y+5y
You can add both like terms and symplify the expression as:
8+10y
The table shows success rates for two computer games sessions. Whose success rate changed the most between session 1 and session 2?
A. Alexis
B. Brent
C. John
D. None of them
Please show explanation I will mark brainliest :)
Answers
Answer:
B. Brent
Step-by-step explanation:
Let us turn the Session 2 scores into fractions so we have common units.
(John) 52% -> \(\frac{52}{100}\)
(Alexis) 57.5% -> \(\frac{575}{1000}\)
(Brent) 39.5% -> \(\frac{395}{1000}\)
Now, we can simplify them.
(John I divide by 2) \(\frac{52}{100}\) -> \(\frac{26}{50}=\frac{13}{25}\)
(Alexis, I divided by 5) \(\frac{575}{1000}\) -> \(\frac{115}{200} =\frac{23}{40}\)
(Brent, I divided by 5) \(\frac{395}{1000}\) -> \(\frac{79}{200}\)
Now subtract Session 2 from Session 1 for each and figure out which one is the largest to answer the question.
(John) \(\frac{2}{3}\) - \(\frac{13}{25}\) = \(\frac{11}{75}\) or about 0.146667
(Alexis) \(\frac{11}{20}\) - \(\frac{23}{40}\) = \(\frac{-1}{40}\) or -0.025
(Brent) \(\frac{7}{10}\) - \(\frac{79}{200}\) = \(\frac{61}{200}\) or 0.305
Since the absolute value of 0.305 is greatest, B. Brent has the largest success rate change.
Given the tile pattern describe how the pattern is growing and find how many tiles will be in step seven
Answers
What is the quotient and the remainder of 21÷6
Answers
Answer:
The quotient is 3, and the remainder is 0.5. So the answer is 3.5!!!
Step-by-step explanation:
Answer: = 3 R 3
21 divided by 6 equals = 3 with a remainder of 3
Step-by-step explanation:
0 3
6 2 1
− 0
2 1
− 1 8
3
sorry bit hard to explain on this note pad thing uwu
When is it appropriate to use the two-sample t-methods instead of the one sample t-methods? Choose the correct answer below. A. Use the two-sample t-methods when a sample was taken from each of two populations (i.e. two groups being compared) and the population standard deviations are not known. Use the one-sample t-methods when a sample was taken from one population. B. Use the two-sample t-methods when a random sample was not taken. Use the one-sample t-methods when a random sample was taken. C. Use the two-sample t-methods when the conditions for inference using the one-sample t-methods aren't satisfied. D. Use the two-sample t-methods when the population standard deviation is known. Use the one-sample t-methods when the population standard deviation is not known.
Answers
Answer:
A. Use the two-sample t-methods when a sample was taken from each of two populations (i.e. two groups being compared) and the population standard deviations are not known.
Step-by-step explanation:
T-distribution:
When the population standard deviation is not known, the t-distribution is used.
If a sample was taken from one population, we use the one-sample method, while if there is a comparison of two populations, the two-sample method is used, and thus, the correct answer is given by option A.
Help pls i dont understand this
Answers
The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The total number of water bottles the company manufactured in February, March, and April.
In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.
Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.
This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.
Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.
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If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. TRUE or FALSE​
Answers
Answer:
True
Step-by-step explanation:
This is true by definition.
What is 1.63 to the third power
Answers
Answer: 4.330747
Step-by-step explanation: Hoped this helped:))
Answer:
4.330747
Step-by-step explanation:
find the surface area of the prism
Answers
Answer: 132 cm cubed
Step-by-step explanation:
0.5*3*4*2=12
10*5=50
4*10=40
3*10=30
30+40+50+12=132 cm cubed
if i compare 0.10__0.01 what would the answer be?
Answers
The answer will be 0. 10 > 0. 01 . Option B
How to compare the valuesGiven the values as;
0.100.01Turn the values into proper fractions
a. 0. 10 = 10/ 100
Reduce to simpler terms
= 10/ 100
= 1/ 10
b. 0. 01 = 1/ 100
a = 1/ 100
b = 1/ 100
This means that both decimals are not of equal proportion and thus a is greater than (>) b
Thus, the answer will be 0. 10 > 0. 01 . Option B
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Jamal wrote the inequality x/16 <6 . Which situation best represented by this inequality Helpppppp
Answers
Given problem;
Inequality equation;
\(\frac{x}{16}\) < 6
Before we solve, let us first translate this problem.
It simply states that for what value(s) of x will the expression be less than 6.
To find this value, we can simply carry out the normal mathematical simplification.
Simply multiply both sides by 16 to reduce the fraction;
16 x (\(\frac{x}{16}\)) < 6 x 16
On the left hand side, 16 will cancel out;
x < 96
Any value for which x is less than 96 will make the solution of this problem less than 6.
For example, 95;
\(\frac{95}{16}\) = 5.93
This value is less than 6
You invested a total of $9000 at 4.5% and 5% simple interest. During one year, the two accounts earned $425.
How much did you invest in each account?
Answers
eg. the first loan is x, the second loan will be (9,000 - x)
First, we need to make an equation based on the problem
first interest + second interest = 492
5% of x + 6% of (9,000 - x) = 492
This is the equation
Second, solve the equation and find out the value of x (first loan)
0.05x + 0.06(9.000 - x) = 492
0.05x + 540 - 0.06x = 492
-0.01x + 540 = 492
-0.01x = 492 - 540
-0.01x = -48
x = -48/-0.01
x = 4,800
Third, find the second loan
9,000 - x
= 9,000 - 4,800
= 4,200
SUMMARY
The first loan that has interest of 5% is $4,800
The second loan that has interest of 6% is $4,200
PLEASE ASAPPP I need thisss to pass
Answers
Answer:
c = 85+20d
c = 245
Step-by-step explanation:
Cost = initial fee + cost per day * number of days
cost = 85 + 20*d where d is the number of days
c = 85+20d
We need to rent for 8 days so d = 8
c = 85+ 20*8
c = 85 + 160
c =245
write y+4=-2(x-1) in slope intercept form
Answers
Answer:
y=2x-6
Step-by-step explanation:
y+4=-2(x-1)
Since the slope intercept form is in the form of:
y=mx+c
Making above equation in this form.
y+4=-2(x-1)
opening bracket
y+4=2x-2
subtracting both side by 4.
y+4-4=2x-2-4
y=2x-6
This equation is the slope intercept form.
Given any two functions f and g, which of the following statements is always true? (1 point)
O If z is in the domain of f. then must be in the domain of f - g.
Olf 2 is in the domain of f and 22 is in the domain of g, then the product, 222, must be in the domain of fg.
O If ac is in the domain of f + g. then I must be in the domain of f and 2 must be in the domain of 9
O fa is not in the domain of then a is not in the domain of g
Answers
Answer:
cccccc
Step-by-step explanation:
Given two functions f and g, we want to see which statement is always true.
The only true statement is the third one:
"If a is in the domain of f + g. then I must be in the domain of f and it must be in the domain of g"
So what we can do, is try to find counterexamples for the given statements, if we can't, then the statements are true.
Note that the statements are really badly written, so I will complete them in a way that makes sense.
a) "If z is in the domain of f. then must be in the domain of f - g"
False, if z is not in the domain of g, then we can't define:
(f - g)(z)
This would happen if:
g = 1/(x - z)
b) "lf 2 is in the domain of f and 22 is in the domain of g, then the product, 222, must be in the domain of fg"
False, lets replace:
2 = z
22 = k
And let's say that:
f(x) = 1/(x - z*k)
g(x) = x
Then we have:
f*g(x) = x/(x - z*k)
Clearly, z*k (or 222 as you wrote it) is not on the domain.
c) "If a is in the domain of f + g. then I must be in the domain of f and it must be in the domain of g"
True, it only can be on the domain of the sum of the two functions if it belongs to the domain of each one.
d) "if a is not in the domain of (f + g) then a is not in the domain of g"
This is false, because a could be in the domain of g and not be in the domain of f.
Then the only true statement is the third one.
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The Stock Market Nadia is a stockbroker. She earns 11% commission each week. Last week, she
sold $5,300 worth of stocks. How much did she make last week in commission? If she averages that
same amount each week, how much did she make in commission in 2011?
Last week, she made $
in commission.
Answers
Answer:
she made $583 commission last week
she made $30313
Step-by-step explanation:
5300 * .11=583
583 * 52 weeks =30316
How many times can 25 go into 145?
Answers
Answer:
5 times or 5.8 times if you want to b specific
Step-by-step explanation:
145 divided by 25= 5.8, simplify that and it equals 5
Answer: 25(x) = 145
x = 5.8
Step-by-step explanation: