Simplify 5/(1/3x^(-2/3)+4)

$\frac{5}{\frac{1}{3} x^{- \frac{2}{3}} + 4}$

Step 1

Simplify the denominator.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5}{\frac{1}{3} \cdot \frac{1}{x^{\frac{2}{3}}} + 4}$

Combine.

$\frac{5}{\frac{1 \cdot 1}{3 x^{\frac{2}{3}}} + 4}$

Multiply $1$ by $1$ .

$\frac{5}{\frac{1}{3 x^{\frac{2}{3}}} + 4}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{3 x^{\frac{2}{3}}}{3 x^{\frac{2}{3}}}$ .

$\frac{5}{\frac{1}{3 x^{\frac{2}{3}}} + 4 \cdot \frac{3 x^{\frac{2}{3}}}{3 x^{\frac{2}{3}}}}$

Combine $4$ and $\frac{3 x^{\frac{2}{3}}}{3 x^{\frac{2}{3}}}$ .

$\frac{5}{\frac{1}{3 x^{\frac{2}{3}}} + \frac{4 (3 x^{\frac{2}{3}})}{3 x^{\frac{2}{3}}}}$

Combine the numerators over the common denominator.

$\frac{5}{\frac{1 + 4 (3 x^{\frac{2}{3}})}{3 x^{\frac{2}{3}}}}$

Reorder terms.

$\frac{5}{\frac{3 \cdot 4 x^{\frac{2}{3}} + 1}{3 x^{\frac{2}{3}}}}$

Multiply $3$ by $4$ .

$\frac{5}{\frac{12 x^{\frac{2}{3}} + 1}{3 x^{\frac{2}{3}}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$5 \frac{3 x^{\frac{2}{3}}}{12 x^{\frac{2}{3}} + 1}$

Step 3

Multiply $5 \frac{3 x^{\frac{2}{3}}}{12 x^{\frac{2}{3}} + 1}$ .

Combine $5$ and $\frac{3 x^{\frac{2}{3}}}{12 x^{\frac{2}{3}} + 1}$ .

$\frac{5 (3 x^{\frac{2}{3}})}{12 x^{\frac{2}{3}} + 1}$

Multiply $3$ by $5$ .

$\frac{15 x^{\frac{2}{3}}}{12 x^{\frac{2}{3}} + 1}$