Simplify ((10x^3)/9)÷(5/(8x^3))

$\frac{10 x^{3}}{9} \div \frac{5}{8 x^{3}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{10 x^{3}}{9} \cdot \frac{8 x^{3}}{5}$

Combine.

$\frac{10 x^{3} (8 x^{3})}{9 \cdot 5}$

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

Move $x^{3}$ .

$\frac{10 (x^{3} x^{3}) \cdot 8}{9 \cdot 5}$

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

$\frac{10 x^{3 + 3} \cdot 8}{9 \cdot 5}$

Add $3$ and $3$ .

$\frac{10 x^{6} \cdot 8}{9 \cdot 5}$

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 x^{6} \cdot 8$ .

$\frac{5 (2 x^{6} \cdot 8)}{9 \cdot 5}$

Cancel the common factors.

Factor $5$ out of $9 \cdot 5$ .

$\frac{5 (2 x^{6} \cdot 8)}{5 \cdot 9}$

Cancel the common factor.

$\frac{5 (2 x^{6} \cdot 8)}{5 \cdot 9}$

Rewrite the expression.

$\frac{2 x^{6} \cdot 8}{9}$

Multiply $8$ by $2$ .

$\frac{16 x^{6}}{9}$