Simplify (x^(-4/7))^7

${(x^{- \frac{4}{7}})}^{7}$

Step 1

Multiply the exponents in ${(x^{- \frac{4}{7}})}^{7}$ .

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

$x^{- \frac{4}{7} \cdot 7}$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{4}{7}$ into the numerator.

$x^{\frac{- 4}{7} \cdot 7}$

Cancel the common factor.

$x^{\frac{- 4}{7} \cdot 7}$

Rewrite the expression.

$x^{- 4}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{4}}$