Power of a Quotient
How to solve the product of powers (am⋅an): formula, 2 examples, and their solutions.
Formula
Formula
(a/b)m = am/bm
(a ≠ 0)
Just like (ab)m formula, power the numbers in the parentheses: am, bm.
Example 1
Example
Solution
Cube x and y2.
So (x/y2)3 = x3/(y2)3.
(y2)3 = y2⋅3 = y6
Power of a Power
So x3/y6 is the answer.
Example 2
Example
Both (a/b)m formula and (ab)m formula powers the numbers in the parentheses.
So you can directly use these two formulas together.
Solution
First square 3, x4, and y.
Then write 32 (x4)2 over y2.
Next, cube y, 2, and x.
Then write y3 over 23 x3.
So the given expresssion is
[(32 (x4)2)/y2] [y3/(23 x3)].
32 = 9
(x4)2 = x4⋅2 = x8
Power of a Power
23 = 8
x8/x3 = x8 - 3 = x5
y3/y2 = y3 - 2 = y
Quotient of Powers
33 = 27
So 9x5y/8 is the answer.