Simplify (-27x^6)^(1/3)

${(- 27 x^{6})}^{\frac{1}{3}}$

Step 1

Simplify the expression.

Apply the product rule to $- 27 x^{6}$ .

${(- 27)}^{\frac{1}{3}} {(x^{6})}^{\frac{1}{3}}$

Rewrite $- 27$ as ${(- 3)}^{3}$ .

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

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

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

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify the expression.

Evaluate the exponent.

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

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

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

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

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 3 x^{2}$