Simplify ((a^3b^5)^2)/(a^6(b^4)^2)

$\frac{{(a^{3} b^{5})}^{2}}{a^{6} {(b^{4})}^{2}}$

Step 1

Simplify the numerator.

Apply the product rule to $a^{3} b^{5}$ .

$\frac{{(a^{3})}^{2} {(b^{5})}^{2}}{a^{6} {(b^{4})}^{2}}$

Multiply the exponents in ${(a^{3})}^{2}$ .

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

$\frac{a^{3 \cdot 2} {(b^{5})}^{2}}{a^{6} {(b^{4})}^{2}}$

Multiply $3$ by $2$ .

$\frac{a^{6} {(b^{5})}^{2}}{a^{6} {(b^{4})}^{2}}$

Multiply the exponents in ${(b^{5})}^{2}$ .

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

$\frac{a^{6} b^{5 \cdot 2}}{a^{6} {(b^{4})}^{2}}$

Multiply $5$ by $2$ .

$\frac{a^{6} b^{10}}{a^{6} {(b^{4})}^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

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

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

$\frac{a^{6} b^{10}}{a^{6} b^{4 \cdot 2}}$

Multiply $4$ by $2$ .

$\frac{a^{6} b^{10}}{a^{6} b^{8}}$

Cancel the common factor of $a^{6}$ .

Cancel the common factor.

$\frac{a^{6} b^{10}}{a^{6} b^{8}}$

Rewrite the expression.

$\frac{b^{10}}{b^{8}}$

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

Factor $b^{8}$ out of $b^{10}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{b^{2}}{1}$

Divide $b^{2}$ by $1$ .

$b^{2}$