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Simplifying with Exponents Answers and Explanations

Power of a Quotient Rule

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Practice simplifying exponents using the Power of a Quotient Rule.

1. Simplify.

(36/49)1/2= 6/7

Raise the numerator and denominator to the power indicated by the exponent:

  • 361/2
  • 491/2

Simplify the numerator and denominator:

  • 361/2 = 6
  • 491/2 = 7

Bring the numerator and denominator together:

6/7

 

 

 

 

 

2. Simplify.

(ab ÷ 180)3= a3b3/5,832,000

Raise the numerator and denominator to the power indicated by the exponent:

  • a3b3
  • 1803

Simplify the numerator and denominator:

  • a3b3= a3b3
  • 1803= 5,832,000

Bring the numerator and denominator together:

a3b3/5,832,000

3. Simplify.

(-5/p)3= -125/p3

Raise the numerator and denominator to the power indicated by the exponent:

  • -53
  • p3

Simplify the numerator and denominator:

  • -53= -125
  • p3= p3

Bring the numerator and denominator together:

-125/p3

4. Simplify.

(-f/g)7= -f 7/g 7

Raise the numerator and denominator to the power indicated by the exponent:

  • -f 7
  • g 7

Simplify the numerator and denominator:

  • -f 7= -f 7
  • g 7 = g 7

Bring the numerator and denominator together:

-f 7/g 7

5. Simplify.

(e/20)-1= 20/e

Raise the numerator and denominator to the power indicated by the exponent:

  • e-1
  • 20-1

Simplify the numerator and denominator:

  • e-1 = 1/e1
  • 20-1= 1/201

Bring the numerator and denominator together:

20/e

6. Simplify.

(xy/Π)10= x10y10 /Π10

Raise the numerator and denominator to the power indicated by the exponent:

  • x10y10
  • Π10

Bring the numerator and denominator together:

x10y10/Π10

 

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