Every Factor Gets the Power

$\left(ab\right)^{2}$ means two copies of the whole product $ab$ multiplied together: $abab$. You can multiply factors in any order, so group the letters: $aabb$, which is $a^{2}b^{2}$.

The power of a product rule says that an exponent on a product in parentheses applies to every factor inside: $\left(ab\right)^{n} = a^{n}b^{n}$. The example shows why. Each copy of $ab$ brings one $a$ and one $b$, so two copies give two of each.

The rule does not work over addition. $\left(a+b\right)^{2}$ is not $a^{2}+b^{2}$. A later lesson in this section shows what $\left(a+b\right)^{2}$ really equals. Factors in a product share the power. Terms in a sum do not.