Simplify (36a^2a^-3b^6)/(4a^6b^-6)

$\frac{36 a^{2} a^{- 3} b^{6}}{4 a^{6} b^{- 6}}$

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

Move $a^{- 3}$ .

$\frac{36 (a^{- 3} a^{2}) b^{6}}{4 a^{6} b^{- 6}}$

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

$\frac{36 a^{- 3 + 2} b^{6}}{4 a^{6} b^{- 6}}$

Add $- 3$ and $2$ .

$\frac{36 a^{- 1} b^{6}}{4 a^{6} b^{- 6}}$

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

$\frac{36 b^{6}}{4 a^{6} b^{- 6} a}$

Multiply $a^{6}$ by $a$ by adding the exponents.

Move $a$ .

$\frac{36 b^{6}}{4 (a \cdot a^{6}) b^{- 6}}$

Multiply $a$ by $a^{6}$ .

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

$\frac{36 b^{6}}{4 (a^{1} a^{6}) b^{- 6}}$

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

$\frac{36 b^{6}}{4 a^{1 + 6} b^{- 6}}$

Add $1$ and $6$ .

$\frac{36 b^{6}}{4 a^{7} b^{- 6}}$

Move $b^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{36 b^{6} b^{6}}{4 a^{7}}$

Multiply $b^{6}$ by $b^{6}$ by adding the exponents.

Move $b^{6}$ .

$\frac{36 (b^{6} b^{6})}{4 a^{7}}$

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

$\frac{36 b^{6 + 6}}{4 a^{7}}$

Add $6$ and $6$ .

$\frac{36 b^{12}}{4 a^{7}}$

Cancel the common factor of $36$ and $4$ .

Factor $4$ out of $36 b^{12}$ .

$\frac{4 (9 b^{12})}{4 a^{7}}$

Cancel the common factors.

Factor $4$ out of $4 a^{7}$ .

$\frac{4 (9 b^{12})}{4 (a^{7})}$

Cancel the common factor.

$\frac{4 (9 b^{12})}{4 a^{7}}$

Rewrite the expression.

$\frac{9 b^{12}}{a^{7}}$