Simplify ((7x^3)/9)/(5/(4x^3))

$\frac{\frac{7 x^{3}}{9}}{\frac{5}{4 x^{3}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 x^{3}}{9} \cdot \frac{4 x^{3}}{5}$

Step 2

Combine.

$\frac{7 x^{3} (4 x^{3})}{9 \cdot 5}$

Step 3

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{7 (x^{3} x^{3}) \cdot 4}{9 \cdot 5}$

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

$\frac{7 x^{3 + 3} \cdot 4}{9 \cdot 5}$

Add $3$ and $3$ .

$\frac{7 x^{6} \cdot 4}{9 \cdot 5}$

Step 4

Multiply $4$ by $7$ .

$\frac{28 x^{6}}{9 \cdot 5}$

Step 5

Multiply $9$ by $5$ .

$\frac{28 x^{6}}{45}$