Simplify (64x^6)^(-1/3)

${(64 x^{6})}^{- \frac{1}{3}}$

Step 1

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

$\frac{1}{{(64 x^{6})}^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

Apply the product rule to $64 x^{6}$ .

$\frac{1}{64^{\frac{1}{3}} {(x^{6})}^{\frac{1}{3}}}$

Rewrite $64$ as $4^{3}$ .

$\frac{1}{{(4^{3})}^{\frac{1}{3}} {(x^{6})}^{\frac{1}{3}}}$

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

$\frac{1}{4^{3 (\frac{1}{3})} {(x^{6})}^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{4^{3 (\frac{1}{3})} {(x^{6})}^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{1}{4^{1} {(x^{6})}^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{1}{4 {(x^{6})}^{\frac{1}{3}}}$

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

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

$\frac{1}{4 x^{6 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{1}{4 x^{3 (2) \frac{1}{3}}}$

Cancel the common factor.

$\frac{1}{4 x^{3 \cdot 2 \frac{1}{3}}}$

Rewrite the expression.

$\frac{1}{4 x^{2}}$