Simplify (2(f^4)^2f^2)/(8f^12)

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

Step 1

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2 {(f^{4})}^{2} f^{2}$ .

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

Cancel the common factors.

Factor $2$ out of $8 f^{12}$ .

$\frac{2 ({(f^{4})}^{2} f^{2})}{2 (4 f^{12})}$

Cancel the common factor.

$\frac{2 ({(f^{4})}^{2} f^{2})}{2 (4 f^{12})}$

Rewrite the expression.

$\frac{{(f^{4})}^{2} f^{2}}{4 f^{12}}$

Step 2

Cancel the common factor of $f^{2}$ and $f^{12}$ .

Factor $f^{2}$ out of ${(f^{4})}^{2} f^{2}$ .

$\frac{f^{2} {(f^{4})}^{2}}{4 f^{12}}$

Cancel the common factors.

Factor $f^{2}$ out of $4 f^{12}$ .

$\frac{f^{2} {(f^{4})}^{2}}{f^{2} (4 f^{10})}$

Cancel the common factor.

$\frac{f^{2} {(f^{4})}^{2}}{f^{2} (4 f^{10})}$

Rewrite the expression.

$\frac{{(f^{4})}^{2}}{4 f^{10}}$

Step 3

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

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

$\frac{f^{4 \cdot 2}}{4 f^{10}}$

Multiply $4$ by $2$ .

$\frac{f^{8}}{4 f^{10}}$

Step 4

Cancel the common factor of $f^{8}$ and $f^{10}$ .

Multiply by $1$ .

$\frac{f^{8} \cdot 1}{4 f^{10}}$

Cancel the common factors.

Factor $f^{8}$ out of $4 f^{10}$ .

$\frac{f^{8} \cdot 1}{f^{8} (4 f^{2})}$

Cancel the common factor.

$\frac{f^{8} \cdot 1}{f^{8} (4 f^{2})}$

Rewrite the expression.

$\frac{1}{4 f^{2}}$