Write with Rational (Fractional) Exponents ( seventh root of -21)^3

${(\sqrt[7]{- 21})}^{3}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{- 21}$ as ${(- 21)}^{\frac{1}{7}}$ .

${({(- 21)}^{\frac{1}{7}})}^{3}$

Step 2

Multiply the exponents in ${({(- 21)}^{\frac{1}{7}})}^{3}$ .

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

${(- 21)}^{\frac{1}{7} \cdot 3}$

Combine $\frac{1}{7}$ and $3$ .

${(- 21)}^{\frac{3}{7}}$