Simplify (x^4)^-2(x^9)^(1/3)

${(x^{4})}^{- 2} {(x^{9})}^{\frac{1}{3}}$

Step 1

Multiply the exponents in ${(x^{4})}^{- 2}$ .

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

$x^{4 \cdot - 2} {(x^{9})}^{\frac{1}{3}}$

Multiply $4$ by $- 2$ .

$x^{- 8} {(x^{9})}^{\frac{1}{3}}$

Step 2

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

$\frac{1}{x^{8}} {(x^{9})}^{\frac{1}{3}}$

Step 3

Multiply the exponents in ${(x^{9})}^{\frac{1}{3}}$ .

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

$\frac{1}{x^{8}} x^{9 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factor.

$\frac{1}{x^{8}} x^{3 \cdot 3 \frac{1}{3}}$

Rewrite the expression.

$\frac{1}{x^{8}} x^{3}$

Step 4

Cancel the common factor of $x^{3}$ .

Factor $x^{3}$ out of $x^{8}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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