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

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

Step 1

Move $x^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

Move $z^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

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

Move $x^{- \frac{1}{3}}$ .

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

Multiply $x^{- \frac{1}{3}}$ by $x$ .

Raise $x$ to the power of $1$ .

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

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

$2 x^{- \frac{1}{3} + 1} z^{3}$

Write $1$ as a fraction with a common denominator.

$2 x^{- \frac{1}{3} + \frac{3}{3}} z^{3}$

Combine the numerators over the common denominator.

$2 x^{\frac{- 1 + 3}{3}} z^{3}$

Add $- 1$ and $3$ .

$2 x^{\frac{2}{3}} z^{3}$

Step 4

Reorder factors in $2 x^{\frac{2}{3}} z^{3}$ .

$2 z^{3} x^{\frac{2}{3}}$