Simplify (10z^(1/3))/(2z^2)

$\frac{10 z^{\frac{1}{3}}}{2 z^{2}}$

Step 1

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

$\frac{10}{2 z^{2} z^{- \frac{1}{3}}}$

Step 2

Multiply $z^{2}$ by $z^{- \frac{1}{3}}$ by adding the exponents.

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

$\frac{10}{2 (z^{- \frac{1}{3}} z^{2})}$

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

$\frac{10}{2 z^{- \frac{1}{3} + 2}}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{10}{2 z^{- \frac{1}{3} + 2 \cdot \frac{3}{3}}}$

Combine $2$ and $\frac{3}{3}$ .

$\frac{10}{2 z^{- \frac{1}{3} + \frac{2 \cdot 3}{3}}}$

Combine the numerators over the common denominator.

$\frac{10}{2 z^{\frac{- 1 + 2 \cdot 3}{3}}}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{10}{2 z^{\frac{- 1 + 6}{3}}}$

Add $- 1$ and $6$ .

$\frac{10}{2 z^{\frac{5}{3}}}$

Step 3

Factor $2$ out of $10$ .

$\frac{2 \cdot 5}{2 z^{\frac{5}{3}}}$

Step 4

Cancel the common factors.

Factor $2$ out of $2 z^{\frac{5}{3}}$ .

$\frac{2 \cdot 5}{2 (z^{\frac{5}{3}})}$

Cancel the common factor.

$\frac{2 \cdot 5}{2 z^{\frac{5}{3}}}$

Rewrite the expression.

$\frac{5}{z^{\frac{5}{3}}}$