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

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

Step 1

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

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

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

Step 2

Simplify the expression.

Multiply $3$ by $2$ .

$\frac{6 x^{5}}{{(x^{2})}^{3}}$

Multiply the exponents in ${(x^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{6 x^{5}}{x^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{6 x^{5}}{x^{6}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{6}$ .

Factor $x^{5}$ out of $6 x^{5}$ .

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

Cancel the common factors.

Factor $x^{5}$ out of $x^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{6}{x}$