Simplify (2(f^4)^2f^3)/(6f^9)

$\frac{2 {(f^{4})}^{2} f^{3}}{6 f^{9}}$

Step 1

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2 {(f^{4})}^{2} f^{3}$ .

$\frac{2 ({(f^{4})}^{2} f^{3})}{6 f^{9}}$

Cancel the common factors.

Factor $2$ out of $6 f^{9}$ .

$\frac{2 ({(f^{4})}^{2} f^{3})}{2 (3 f^{9})}$

Cancel the common factor.

$\frac{2 ({(f^{4})}^{2} f^{3})}{2 (3 f^{9})}$

Rewrite the expression.

$\frac{{(f^{4})}^{2} f^{3}}{3 f^{9}}$

$\frac{{(f^{4})}^{2} f^{3}}{3 f^{9}}$

$\frac{{(f^{4})}^{2} f^{3}}{3 f^{9}}$

Step 2

Cancel the common factor of $f^{3}$ and $f^{9}$ .

Factor $f^{3}$ out of ${(f^{4})}^{2} f^{3}$ .

$\frac{f^{3} {(f^{4})}^{2}}{3 f^{9}}$

Cancel the common factors.

Factor $f^{3}$ out of $3 f^{9}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 3

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

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

$\frac{f^{4 \cdot 2}}{3 f^{6}}$

Multiply $4$ by $2$ .

$\frac{f^{8}}{3 f^{6}}$

$\frac{f^{8}}{3 f^{6}}$

Step 4

Cancel the common factor of $f^{8}$ and $f^{6}$ .

Factor $f^{6}$ out of $f^{8}$ .

$\frac{f^{6} f^{2}}{3 f^{6}}$

Cancel the common factors.

Factor $f^{6}$ out of $3 f^{6}$ .

$\frac{f^{6} f^{2}}{f^{6} \cdot 3}$

Cancel the common factor.

$\frac{f^{6} f^{2}}{f^{6} \cdot 3}$

Rewrite the expression.

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

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

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

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