Power of a Product Property

Property If $m$ is a real number with $x \neq 0$ and $y \neq 0$, then $(xy)^m = x^m y^m$.

Examples In $(3x^2y^5)^2$, the exponent 2 applies to everything: $3^2 \cdot (x^2)^2 \cdot (y^5)^2 = 9x^4y^{10}$. Be careful with negatives: $( 4a^3)^2 = ( 4)^2 \cdot (a^3)^2 = 16a^6$. If a square garden has a side length of $5y$ feet, its area is $(5y)^2 = 25y^2$ square feet.

Explanation Welcome to the 'share the power' party! The exponent outside the parentheses applies to every single factor inside. You have to distribute the power to each number and variable. Don't forget anyone, or your answer will be wrong! It ensures every part of the product gets raised to the same power.