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mixer [17]
3 years ago
10

Simplify using only POSITIVE exponents:

Mathematics
1 answer:
pickupchik [31]3 years ago
3 0

So here are a few rules with exponents that you should know:

  1. Multiplying exponents of the same base: x^m*x^n=x^{m+n}
  2. Dividing exponents of the same base: x^m\div x^n=x^{m-n}
  3. Powering a power to a power: (x^m)^n=x^{m*n}
  4. Converting a negative exponent to a positive one: x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m
<h2>1.</h2>

Firstly, solve the outside exponent:

(2x^3y^7)^{-2}=2^{-2}x^{3*-2}y^{7*-2}=2^{-2}x^{-6}y^{-14}

Next, convert the negative exponents into positive ones:

2^{-2}x^{-6}y^{-14}=\frac{1}{2^2x^6y^{14}}=\frac{1}{4x^6y^{14}}

<u>Your final answer is \frac{1}{4x^6y^{14}}</u>

<h2>2.</h2>

For this, just divide:

\frac{12x^5y^3}{4x^{-1}}=\frac{12}{4}x^{5-(-1)}y^{3-0}=3x^6y^3

<u>Your final answer is 3x^6y^3</u>

<h2>3.</h2>

For this, convert all negative exponents into positive ones:

\frac{r^{-7}b^{-8}}{t^{-4}w}=\frac{t^4}{r^7b^8w}

<u>Your final answer is \frac{t^4}{r^7b^8w}</u>

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Answer: \frac{20}{3}\ minutes or 6 \frac{2}{3}\ minutes

Step-by-step explanation:

For this exercise you can convert the mixed number to an improper fraction:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained and the numerator of the fraction (This will be the new numerator).

3. The denominator does not change.

Then:

23\frac{1}{3}= \frac{(23*3)+1}{3}= \frac{70}{3}\ minutes

You know that he had 30 minutes in time-out, he counted spots on the ceiling for \frac{70}{3} minutes and the rest of the time he made faces at his stuffed tiger.

Then, in order to calculate the time Calvin spent making faces at his stuffed tiger, you need to subract 30 minutes and \frac{70}{3} minutes:

30\ min-\frac{70}{3}=(\frac{3(30)-70}{3})=\frac{20}{3}\ minutes or 6 \frac{2}{3}\ minutes

7 0
3 years ago
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The answer should be
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The answer is 54 cubes.

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