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

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

Step 1

Combine.

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

Step 2

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

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

Step 3

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x^{5} \cdot 3$ .

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

Cancel the common factors.

Factor $2$ out of $5 \cdot 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the expression.

Multiply $5$ by $2$ .

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

Move $3$ to the left of $x^{5}$ .

$\frac{3 x^{5}}{10}$