Simplify (8x^15)^(-1/3)

${(8 x^{15})}^{- \frac{1}{3}}$

Step 1

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

$\frac{1}{{(8 x^{15})}^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

Apply the product rule to $8 x^{15}$ .

$\frac{1}{8^{\frac{1}{3}} {(x^{15})}^{\frac{1}{3}}}$

Rewrite $8$ as $2^{3}$ .

$\frac{1}{{(2^{3})}^{\frac{1}{3}} {(x^{15})}^{\frac{1}{3}}}$

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

$\frac{1}{2^{3 (\frac{1}{3})} {(x^{15})}^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{2^{3 (\frac{1}{3})} {(x^{15})}^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{1}{2^{1} {(x^{15})}^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{1}{2 {(x^{15})}^{\frac{1}{3}}}$

Multiply the exponents in ${(x^{15})}^{\frac{1}{3}}$ .

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

$\frac{1}{2 x^{15 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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