Simplify ((-5)^(2/3))^(3/4)

${({(- 5)}^{\frac{2}{3}})}^{\frac{3}{4}}$

Step 1

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

${(- 5)}^{\frac{2}{3} \cdot \frac{3}{4}}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

${(- 5)}^{\frac{1}{3} \cdot \frac{3}{2}}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 5)}^{\frac{1}{3} \cdot \frac{3}{2}}$

Rewrite the expression.

${(- 5)}^{\frac{1}{2}}$