# How do you simplify (5a^(1/7)b^(5/7))^3?

Oct 15, 2016

$125 {a}^{\frac{3}{7}} {b}^{\frac{15}{7}}$

#### Explanation:

${\left(5 {a}^{\frac{1}{7}} {b}^{\frac{5}{7}}\right)}^{3}$

Use the exponent rule ${\left({x}^{a}\right)}^{b} = {x}^{a b}$

First, recall that when there is no exponent written, there is an exponent of $\textcolor{red}{1}$.

${\left({5}^{\textcolor{red}{1}} {a}^{\frac{1}{7}} {b}^{\frac{5}{7}}\right)}^{\textcolor{b l u e}{3}}$

Each part inside the fraction must be "raised to the power" 3. The exponents are then multiplied.

5^(color(red)1*color(blue)3)a^(1/7*color(blue)3)b^(5/7*color(blue)3

$\frac{1}{7} \cdot 3 = \frac{1}{7} \cdot \frac{3}{1} = \frac{3}{7}$ and $\frac{5}{7} \cdot 3 = \frac{5}{7} \cdot \frac{3}{1} = \frac{15}{7}$

${5}^{3} {a}^{\frac{3}{7}} {b}^{\frac{15}{7}}$

${5}^{3} = 5 \cdot 5 \cdot 5 = 125$

$125 {a}^{\frac{3}{7}} {b}^{\frac{15}{7}}$