Simplify (3a^2)/(3(a^2)^4)

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

Step 1

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{a^{2}}{{(a^{2})}^{4}}$

Step 2

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

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

$\frac{a^{2}}{a^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{a^{2}}{a^{8}}$

Step 3

Cancel the common factor of $a^{2}$ and $a^{8}$ .

Multiply by $1$ .

$\frac{a^{2} \cdot 1}{a^{8}}$

Cancel the common factors.

Factor $a^{2}$ out of $a^{8}$ .

$\frac{a^{2} \cdot 1}{a^{2} a^{6}}$

Cancel the common factor.

$\frac{a^{2} \cdot 1}{a^{2} a^{6}}$

Rewrite the expression.

$\frac{1}{a^{6}}$