Simplify (m^(2/3)n^2)/(m^-1n^3)

$\frac{m^{\frac{2}{3}} n^{2}}{m^{- 1} n^{3}}$

Step 1

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

$\frac{m^{\frac{2}{3}} n^{2} m}{n^{3}}$

Step 2

Multiply $m^{\frac{2}{3}}$ by $m$ by adding the exponents.

Move $m$ .

$\frac{m \cdot m^{\frac{2}{3}} n^{2}}{n^{3}}$

Multiply $m$ by $m^{\frac{2}{3}}$ .

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

$\frac{m^{1} m^{\frac{2}{3}} n^{2}}{n^{3}}$

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

$\frac{m^{1 + \frac{2}{3}} n^{2}}{n^{3}}$

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

$\frac{m^{\frac{3}{3} + \frac{2}{3}} n^{2}}{n^{3}}$

Combine the numerators over the common denominator.

$\frac{m^{\frac{3 + 2}{3}} n^{2}}{n^{3}}$

Add $3$ and $2$ .

$\frac{m^{\frac{5}{3}} n^{2}}{n^{3}}$

Step 3

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

$\frac{n^{2} m^{\frac{5}{3}}}{n^{3}}$

Step 4

Cancel the common factors.

Factor $n^{2}$ out of $n^{3}$ .

$\frac{n^{2} m^{\frac{5}{3}}}{n^{2} n}$

Cancel the common factor.

$\frac{n^{2} m^{\frac{5}{3}}}{n^{2} n}$

Rewrite the expression.

$\frac{m^{\frac{5}{3}}}{n}$