Simplify ((5ab)^3)/(30a^-6b^-7)

$\frac{{(5 a b)}^{3}}{30 a^{- 6} b^{- 7}}$

Simplify.

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

$\frac{{(5 a b)}^{3} a^{6}}{30 b^{- 7}}$

Move $b^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(5 a b)}^{3} a^{6} b^{7}}{30}$

Simplify the numerator.

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Apply the product rule to $5 a b$ .

$\frac{{(5 a)}^{3} b^{3} a^{6} b^{7}}{30}$

Multiply $b^{3}$ by $b^{7}$ by adding the exponents.

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Move $b^{7}$ .

$\frac{{(5 a)}^{3} (b^{7} b^{3}) a^{6}}{30}$

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

$\frac{{(5 a)}^{3} b^{7 + 3} a^{6}}{30}$

Add $7$ and $3$ .

$\frac{{(5 a)}^{3} b^{10} a^{6}}{30}$

Apply the product rule to $5 a$ .

$\frac{5^{3} a^{3} b^{10} a^{6}}{30}$

Raise $5$ to the power of $3$ .

$\frac{125 a^{3} b^{10} a^{6}}{30}$

Multiply $a^{3}$ by $a^{6}$ by adding the exponents.

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Move $a^{6}$ .

$\frac{125 (a^{6} a^{3}) b^{10}}{30}$

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

$\frac{125 a^{6 + 3} b^{10}}{30}$

Add $6$ and $3$ .

$\frac{125 a^{9} b^{10}}{30}$

Cancel the common factor of $125$ and $30$ .

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Factor $5$ out of $125 a^{9} b^{10}$ .

$\frac{5 (25 a^{9} b^{10})}{30}$

Cancel the common factors.

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Factor $5$ out of $30$ .

$\frac{5 (25 a^{9} b^{10})}{5 (6)}$

Cancel the common factor.

$\frac{5 (25 a^{9} b^{10})}{5 \cdot 6}$

Rewrite the expression.

$\frac{25 a^{9} b^{10}}{6}$

Simplify ((5ab)^3)/(30a^-6b^-7)

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