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

$\frac{4 x^{2}}{- 3 x^{\frac{4}{3}}}$

Move $x^{\frac{4}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{4 x^{2} x^{- \frac{4}{3}}}{- 3}$

Multiply $x^{2}$ by $x^{- \frac{4}{3}}$ by adding the exponents.

Move $x^{- \frac{4}{3}}$ .

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

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

$\frac{4 x^{- \frac{4}{3} + 2}}{- 3}$

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{4 x^{\frac{- 4 + 6}{3}}}{- 3}$

Add $- 4$ and $6$ .

$\frac{4 x^{\frac{2}{3}}}{- 3}$

Move the negative in front of the fraction.

$- \frac{4 x^{\frac{2}{3}}}{3}$