Definition: (x/y)a = xa/ya

When this works: A quotient in parentheses that is raised to a power.

Examples of when to use the Power of a Quotient Rule:

  • (x/5)4
  • (6/e)10
  • (ab ÷ 180)3

Notice that the numerator and denominator can be different.

1. Power of a Quotient Rule and Constants

Simplify (18/6)4.

(18/6)4 = 184/64 = 104976/1296 = 81

Why Does this Work?

Rewrite (18/6)4:

(18/6)4 = (18/6) * (18/6) * (18/6) * (18/6)

Multiply:

104976/1296 = 81


2. Power of a Quotient Rule and Variables

Simplify (j/k)3.

(j/k)3 = j3/k3

Why does this work?

Rewrite (j/k)3

(j/k)3 = (j/k)*(j/k)*(j/k)Multiply numerators and multiply denonominators:

j * j * j = j3

k * k * k = k3

Bring the numerator and denominator together.

j3/k3

3. Power of a Quotient Rule Practice

Power of a Quotient Rule: (x/y)a = xa/ya

Simplify:

1. (36/49)1/2

2. (ab ÷ 180)3

3. (-5/p)3

4. (-f/g)7

5. (e/20)-1

6. (xy/Π)10

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