Simplify ((5x^3)/4)÷((15x)/8)

$\frac{5 x^{3}}{4} \div \frac{15 x}{8}$

To divide by a fraction, multiply by its reciprocal.

$\frac{5 x^{3}}{4} \cdot \frac{8}{15 x}$

Combine.

$\frac{5 x^{3} \cdot 8}{4 (15 x)}$

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5 x^{3} \cdot 8$ .

$\frac{5 (x^{3} \cdot 8)}{4 (15 x)}$

Cancel the common factors.

Factor $5$ out of $4 (15 x)$ .

$\frac{5 (x^{3} \cdot 8)}{5 (4 (3 x))}$

Cancel the common factor.

$\frac{5 (x^{3} \cdot 8)}{5 (4 (3 x))}$

Rewrite the expression.

$\frac{x^{3} \cdot 8}{4 (3 x)}$

$\frac{x^{3} \cdot 8}{4 (3 x)}$

$\frac{x^{3} \cdot 8}{4 (3 x)}$

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $x^{3} \cdot 8$ .

$\frac{x (x^{2} \cdot 8)}{4 (3 x)}$

Cancel the common factors.

Factor $x$ out of $4 (3 x)$ .

$\frac{x (x^{2} \cdot 8)}{x (4 \cdot (3))}$

Cancel the common factor.

$\frac{x (x^{2} \cdot 8)}{x (4 \cdot (3))}$

Rewrite the expression.

$\frac{x^{2} \cdot 8}{4 \cdot (3)}$

$\frac{x^{2} \cdot 8}{4 \cdot (3)}$

$\frac{x^{2} \cdot 8}{4 \cdot (3)}$

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $x^{2} \cdot 8$ .

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

Cancel the common factors.

Factor $4$ out of $4 \cdot (3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x^{2} \cdot 2}{3}$

$\frac{x^{2} \cdot 2}{3}$

$\frac{x^{2} \cdot 2}{3}$

Move $2$ to the left of $x^{2}$ .

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

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