Simplify (x^2)/(x+8)*(2x^2)/(2x+16)

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 x + 16}$

Step 1

Factor $2$ out of $2 x + 16$ .

Factor $2$ out of $2 x$ .

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 (x) + 16}$

Factor $2$ out of $16$ .

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 x + 2 \cdot 8}$

Factor $2$ out of $2 x + 2 \cdot 8$ .

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 (x + 8)}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x^{2}}{x + 8} \cdot \frac{2 x^{2}}{2 (x + 8)}$

Rewrite the expression.

$\frac{x^{2}}{x + 8} \cdot \frac{x^{2}}{x + 8}$

Step 3

Multiply $\frac{x^{2}}{x + 8} \cdot \frac{x^{2}}{x + 8}$ .

Multiply $\frac{x^{2}}{x + 8}$ by $\frac{x^{2}}{x + 8}$ .

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

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

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

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

Add $2$ and $2$ .

$\frac{x^{4}}{(x + 8) (x + 8)}$

Raise $x + 8$ to the power of $1$ .

$\frac{x^{4}}{{(x + 8)}^{1} (x + 8)}$

Raise $x + 8$ to the power of $1$ .

$\frac{x^{4}}{{(x + 8)}^{1} {(x + 8)}^{1}}$

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

$\frac{x^{4}}{{(x + 8)}^{1 + 1}}$

Add $1$ and $1$ .

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