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