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

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

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $16$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

$\frac{{(x + 8)}^{1} (x + 8)}{x^{2} x^{2}}$

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

$\frac{{(x + 8)}^{1} {(x + 8)}^{1}}{x^{2} x^{2}}$

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

$\frac{{(x + 8)}^{1 + 1}}{x^{2} x^{2}}$

Add $1$ and $1$ .

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

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

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

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

Add $2$ and $2$ .

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