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