Question

How do you simplify `(3u^{2} v^{2} )^{2}`?

Answer 1

`9u^4v^4`

Explanation:

Two properties of exponents are combined in this problem. The Power of a Product Property states that if a product is raised to a power, then all factors must be individually raised to that power.
`(ab)^n = a^nb^n`
The Power of a Power Property states that if a power expression is raised to another power, the base remains the same and the powers are multiplied.
`(a^n)^m = a^(nm)`
Applying these two properties yields the simplified expression:
`(3u^2v^2)^2`
`3^2u^(2*2)v^(2*2)`
`9u^4v^4`