Simplify (m^3)^-1(x^(1/3))^(1/4)

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

Multiply the exponents in ${(m^{3})}^{- 1}$ .

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

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

Multiply $3$ by $- 1$ .

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

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

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

Multiply the exponents in ${(x^{\frac{1}{3}})}^{\frac{1}{4}}$ .

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

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

Multiply $\frac{1}{3} \cdot \frac{1}{4}$ .

Multiply $\frac{1}{3}$ by $\frac{1}{4}$ .

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

Multiply $3$ by $4$ .

$\frac{1}{m^{3}} x^{\frac{1}{12}}$

Combine $\frac{1}{m^{3}}$ and $x^{\frac{1}{12}}$ .

$\frac{x^{\frac{1}{12}}}{m^{3}}$