Simplify ((2x^2)^3)/(12x^4)

$\frac{{(2 x^{2})}^{3}}{12 x^{4}}$

Step 1

Simplify the numerator.

Apply the product rule to $2 x^{2}$ .

$\frac{2^{3} {(x^{2})}^{3}}{12 x^{4}}$

Raise $2$ to the power of $3$ .

$\frac{8 {(x^{2})}^{3}}{12 x^{4}}$

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

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

$\frac{8 x^{2 \cdot 3}}{12 x^{4}}$

Multiply $2$ by $3$ .

$\frac{8 x^{6}}{12 x^{4}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $8$ and $12$ .

Factor $4$ out of $8 x^{6}$ .

$\frac{4 (2 x^{6})}{12 x^{4}}$

Cancel the common factors.

Factor $4$ out of $12 x^{4}$ .

$\frac{4 (2 x^{6})}{4 (3 x^{4})}$

Cancel the common factor.

$\frac{4 (2 x^{6})}{4 (3 x^{4})}$

Rewrite the expression.

$\frac{2 x^{6}}{3 x^{4}}$

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $2 x^{6}$ .

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

Cancel the common factors.

Factor $x^{4}$ out of $3 x^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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