Simplify (6ab)/((a^0b^2)^4)

$\frac{6 a b}{{(a^{0} b^{2})}^{4}}$

Step 1

Simplify the denominator.

Apply the product rule to $a^{0} b^{2}$ .

$\frac{6 a b}{{(a^{0})}^{4} {(b^{2})}^{4}}$

Multiply the exponents in ${(a^{0})}^{4}$ .

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

$\frac{6 a b}{a^{0 \cdot 4} {(b^{2})}^{4}}$

Multiply $0$ by $4$ .

$\frac{6 a b}{a^{0} {(b^{2})}^{4}}$

Anything raised to $0$ is $1$ .

$\frac{6 a b}{1 {(b^{2})}^{4}}$

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

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

$\frac{6 a b}{1 b^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{6 a b}{1 b^{8}}$

Multiply $b^{8}$ by $1$ .

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

Step 2

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

Factor $b$ out of $6 a b$ .

$\frac{b (6 a)}{b^{8}}$

Cancel the common factors.

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

$\frac{b (6 a)}{b \cdot b^{7}}$

Cancel the common factor.

$\frac{b (6 a)}{b \cdot b^{7}}$

Rewrite the expression.

$\frac{6 a}{b^{7}}$