Simplify (a^2b^-1(ab^2)^3)/(a^-3b^4)

$\frac{a^{2} b^{- 1} {(a b^{2})}^{3}}{a^{- 3} b^{4}}$

Move $b^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Multiply $b^{4}$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b^{4}$ .

Raise $b$ to the power of $1$ .

$\frac{a^{2} {(a b^{2})}^{3}}{a^{- 3} (b^{1} b^{4})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{2} {(a b^{2})}^{3}}{a^{- 3} b^{1 + 4}}$

Add $1$ and $4$ .

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

Move $a^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $3$ and $2$ .

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

Simplify the numerator.

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

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

Multiply $a^{5}$ by $a^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $5$ and $3$ .

$\frac{a^{8} {(b^{2})}^{3}}{b^{5}}$

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

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

$\frac{a^{8} b^{2 \cdot 3}}{b^{5}}$

Multiply $2$ by $3$ .

$\frac{a^{8} b^{6}}{b^{5}}$

Cancel the common factor of $b^{6}$ and $b^{5}$ .

Factor $b^{5}$ out of $a^{8} b^{6}$ .

$\frac{b^{5} (a^{8} b)}{b^{5}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{b^{5} (a^{8} b)}{b^{5} \cdot 1}$

Cancel the common factor.

$\frac{b^{5} (a^{8} b)}{b^{5} \cdot 1}$

Rewrite the expression.

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

Divide $a^{8} b$ by $1$ .

$a^{8} b$

Simplify (a^2b^-1(ab^2)^3)/(a^-3b^4)

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