Simplify (-32q^7)^(3/5)

${(- 32 q^{7})}^{\frac{3}{5}}$

Step 1

Simplify the expression.

Apply the product rule to $- 32 q^{7}$ .

${(- 32)}^{\frac{3}{5}} {(q^{7})}^{\frac{3}{5}}$

Rewrite $- 32$ as ${(- 2)}^{5}$ .

${({(- 2)}^{5})}^{\frac{3}{5}} {(q^{7})}^{\frac{3}{5}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(- 2)}^{5 (\frac{3}{5})} {(q^{7})}^{\frac{3}{5}}$

Step 2

Cancel the common factor of $5$ .

Cancel the common factor.

${(- 2)}^{5 (\frac{3}{5})} {(q^{7})}^{\frac{3}{5}}$

Rewrite the expression.

${(- 2)}^{3} {(q^{7})}^{\frac{3}{5}}$

Step 3

Simplify the expression.

Raise $- 2$ to the power of $3$ .

$- 8 {(q^{7})}^{\frac{3}{5}}$

Multiply the exponents in ${(q^{7})}^{\frac{3}{5}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 8 q^{7 (\frac{3}{5})}$

Multiply $7 (\frac{3}{5})$ .

Combine $7$ and $\frac{3}{5}$ .

$- 8 q^{\frac{7 \cdot 3}{5}}$

Multiply $7$ by $3$ .

$- 8 q^{\frac{21}{5}}$