Simplify (x^(3/5))^(-1/6)

${(x^{\frac{3}{5}})}^{- \frac{1}{6}}$

Step 1

Multiply the exponents in ${(x^{\frac{3}{5}})}^{- \frac{1}{6}}$ .

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

$x^{\frac{3}{5} (- \frac{1}{6})}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$x^{\frac{3}{5} \cdot \frac{- 1}{6}}$

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x^{\frac{1}{5} \cdot \frac{- 1}{2}}$

Multiply $\frac{1}{5}$ by $\frac{- 1}{2}$ .

$x^{\frac{- 1}{5 \cdot 2}}$

Multiply $5$ by $2$ .

$x^{\frac{- 1}{10}}$

Move the negative in front of the fraction.

$x^{- \frac{1}{10}}$

Step 2

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

$\frac{1}{x^{\frac{1}{10}}}$