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

Oct 7, 2016

$9 {u}^{4} {v}^{4}$

#### 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.
${\left(a b\right)}^{n} = {a}^{n} {b}^{n}$
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.
${\left({a}^{n}\right)}^{m} = {a}^{n m}$
Applying these two properties yields the simplified expression:
${\left(3 {u}^{2} {v}^{2}\right)}^{2}$
${3}^{2} {u}^{2 \cdot 2} {v}^{2 \cdot 2}$
$9 {u}^{4} {v}^{4}$