Divide (11x^3)/(7x^(7/3))

$\frac{11 x^{3}}{7 x^{\frac{7}{3}}}$

Step 1

Move $x^{\frac{7}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{11 x^{3} x^{- \frac{7}{3}}}{7}$

Step 2

Multiply $x^{3}$ by $x^{- \frac{7}{3}}$ by adding the exponents.

Move $x^{- \frac{7}{3}}$ .

$\frac{11 (x^{- \frac{7}{3}} x^{3})}{7}$

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

$\frac{11 x^{- \frac{7}{3} + 3}}{7}$

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

$\frac{11 x^{- \frac{7}{3} + 3 \cdot \frac{3}{3}}}{7}$

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

$\frac{11 x^{- \frac{7}{3} + \frac{3 \cdot 3}{3}}}{7}$

Combine the numerators over the common denominator.

$\frac{11 x^{\frac{- 7 + 3 \cdot 3}{3}}}{7}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{11 x^{\frac{- 7 + 9}{3}}}{7}$

Add $- 7$ and $9$ .

$\frac{11 x^{\frac{2}{3}}}{7}$