Simplify ((7x^2)/3)/(5/(4x))

$\frac{\frac{7 x^{2}}{3}}{\frac{5}{4 x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 x^{2}}{3} \cdot \frac{4 x}{5}$

Step 2

Combine.

$\frac{7 x^{2} (4 x)}{3 \cdot 5}$

Step 3

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$\frac{7 (x \cdot x^{2}) \cdot 4}{3 \cdot 5}$

Multiply $x$ by $x^{2}$ .

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

$\frac{7 (x^{1} x^{2}) \cdot 4}{3 \cdot 5}$

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

$\frac{7 x^{1 + 2} \cdot 4}{3 \cdot 5}$

Add $1$ and $2$ .

$\frac{7 x^{3} \cdot 4}{3 \cdot 5}$

Step 4

Multiply $4$ by $7$ .

$\frac{28 x^{3}}{3 \cdot 5}$

Step 5

Multiply $3$ by $5$ .

$\frac{28 x^{3}}{15}$