Simplify (3n^(5/3))/(4n^2)

$\frac{3 n^{\frac{5}{3}}}{4 n^{2}}$

Move $n^{\frac{5}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{3}{4 n^{2} n^{- \frac{5}{3}}}$

Multiply $n^{2}$ by $n^{- \frac{5}{3}}$ by adding the exponents.

Move $n^{- \frac{5}{3}}$ .

$\frac{3}{4 (n^{- \frac{5}{3}} n^{2})}$

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

$\frac{3}{4 n^{- \frac{5}{3} + 2}}$

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

$\frac{3}{4 n^{- \frac{5}{3} + 2 \cdot \frac{3}{3}}}$

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

$\frac{3}{4 n^{- \frac{5}{3} + \frac{2 \cdot 3}{3}}}$

Combine the numerators over the common denominator.

$\frac{3}{4 n^{\frac{- 5 + 2 \cdot 3}{3}}}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{3}{4 n^{\frac{- 5 + 6}{3}}}$

Add $- 5$ and $6$ .

$\frac{3}{4 n^{\frac{1}{3}}}$