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

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

Step 1

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

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

Step 2

Combine $2$ and $\frac{1}{x^{\frac{1}{3}}}$ .

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

Step 3

Simplify the expression.

Apply the product rule to $\frac{2}{x^{\frac{1}{3}}}$ .

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

Raise $2$ to the power of $4$ .

$x \frac{16}{{(x^{\frac{1}{3}})}^{4}}$

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

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

$x \frac{16}{x^{\frac{1}{3} \cdot 4}}$

Combine $\frac{1}{3}$ and $4$ .

$x \frac{16}{x^{\frac{4}{3}}}$

Step 4

Combine $x$ and $\frac{16}{x^{\frac{4}{3}}}$ .

$\frac{x \cdot 16}{x^{\frac{4}{3}}}$

Step 5

Move $x^{1}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{16}{x^{\frac{4}{3}} x^{- 1}}$

Step 6

Multiply $x^{\frac{4}{3}}$ by $x^{- 1}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{16}{x^{\frac{4}{3} - 1}}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{16}{x^{\frac{4}{3} - 1 \cdot \frac{3}{3}}}$

Combine $- 1$ and $\frac{3}{3}$ .

$\frac{16}{x^{\frac{4}{3} + \frac{- 1 \cdot 3}{3}}}$

Combine the numerators over the common denominator.

$\frac{16}{x^{\frac{4 - 1 \cdot 3}{3}}}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$\frac{16}{x^{\frac{4 - 3}{3}}}$

Subtract $3$ from $4$ .

$\frac{16}{x^{\frac{1}{3}}}$