Pre-Algebra Examples

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

Step 1

Multiply the exponents in ${(x^{2})}^{4}$ .

Tap for more steps...

Step 1.1

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

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

Step 1.2

Multiply $2$ by $4$ .

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $2 x$ .

$\frac{x^{8}}{2^{3} x^{3}}$

Step 2.2

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

$\frac{x^{8}}{8 x^{3}}$

Step 3

Cancel the common factor of $x^{8}$ and $x^{3}$ .

Tap for more steps...

Step 3.1

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

$\frac{x^{3} x^{5}}{8 x^{3}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{x^{5}}{8}$