Simplify ((u^4v^3)^-3(-3uv^5)^4)/((6u^2v)^5)

$\frac{{(u^{4} v^{3})}^{- 3} {(- 3 u v^{5})}^{4}}{{(6 u^{2} v)}^{5}}$

Move ${(u^{4} v^{3})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(- 3 u v^{5})}^{4}}{{(6 u^{2} v)}^{5} {(u^{4} v^{3})}^{3}}$

Simplify the numerator.

Apply the product rule to $- 3 u v^{5}$ .

$\frac{{(- 3 u)}^{4} {(v^{5})}^{4}}{{(6 u^{2} v)}^{5} {(u^{4} v^{3})}^{3}}$

Apply the product rule to $- 3 u$ .

$\frac{{(- 3)}^{4} u^{4} {(v^{5})}^{4}}{{(6 u^{2} v)}^{5} {(u^{4} v^{3})}^{3}}$

Raise $- 3$ to the power of $4$ .

$\frac{81 u^{4} {(v^{5})}^{4}}{{(6 u^{2} v)}^{5} {(u^{4} v^{3})}^{3}}$

Multiply the exponents in ${(v^{5})}^{4}$ .

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

$\frac{81 u^{4} v^{5 \cdot 4}}{{(6 u^{2} v)}^{5} {(u^{4} v^{3})}^{3}}$

Multiply $5$ by $4$ .

$\frac{81 u^{4} v^{20}}{{(6 u^{2} v)}^{5} {(u^{4} v^{3})}^{3}}$

Simplify the denominator.

Apply the product rule to $6 u^{2} v$ .

$\frac{81 u^{4} v^{20}}{{(6 u^{2})}^{5} v^{5} {(u^{4} v^{3})}^{3}}$

Apply the product rule to $u^{4} v^{3}$ .

$\frac{81 u^{4} v^{20}}{{(6 u^{2})}^{5} v^{5} {(u^{4})}^{3} {(v^{3})}^{3}}$

Apply the product rule to $6 u^{2}$ .

$\frac{81 u^{4} v^{20}}{6^{5} {(u^{2})}^{5} v^{5} {(u^{4})}^{3} {(v^{3})}^{3}}$

Raise $6$ to the power of $5$ .

$\frac{81 u^{4} v^{20}}{7776 {(u^{2})}^{5} v^{5} {(u^{4})}^{3} {(v^{3})}^{3}}$

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

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

$\frac{81 u^{4} v^{20}}{7776 u^{2 \cdot 5} v^{5} {(u^{4})}^{3} {(v^{3})}^{3}}$

Multiply $2$ by $5$ .

$\frac{81 u^{4} v^{20}}{7776 u^{10} v^{5} {(u^{4})}^{3} {(v^{3})}^{3}}$

Multiply the exponents in ${(u^{4})}^{3}$ .

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

$\frac{81 u^{4} v^{20}}{7776 u^{10} v^{5} u^{4 \cdot 3} {(v^{3})}^{3}}$

Multiply $4$ by $3$ .

$\frac{81 u^{4} v^{20}}{7776 u^{10} v^{5} u^{12} {(v^{3})}^{3}}$

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

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

$\frac{81 u^{4} v^{20}}{7776 u^{10} v^{5} u^{12} v^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{81 u^{4} v^{20}}{7776 u^{10} v^{5} u^{12} v^{9}}$

Combine exponents.

Multiply $u^{10}$ by $u^{12}$ by adding the exponents.

Move $u^{12}$ .

$\frac{81 u^{4} v^{20}}{7776 (u^{12} u^{10}) v^{5} v^{9}}$

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

$\frac{81 u^{4} v^{20}}{7776 u^{12 + 10} v^{5} v^{9}}$

Add $12$ and $10$ .

$\frac{81 u^{4} v^{20}}{7776 u^{22} v^{5} v^{9}}$

Multiply $v^{5}$ by $v^{9}$ by adding the exponents.

Move $v^{9}$ .

$\frac{81 u^{4} v^{20}}{7776 u^{22} (v^{9} v^{5})}$

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

$\frac{81 u^{4} v^{20}}{7776 u^{22} v^{9 + 5}}$

Add $9$ and $5$ .

$\frac{81 u^{4} v^{20}}{7776 u^{22} v^{14}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $81$ and $7776$ .

Factor $81$ out of $81 u^{4} v^{20}$ .

$\frac{81 (u^{4} v^{20})}{7776 u^{22} v^{14}}$

Cancel the common factors.

Factor $81$ out of $7776 u^{22} v^{14}$ .

$\frac{81 (u^{4} v^{20})}{81 (96 u^{22} v^{14})}$

Cancel the common factor.

$\frac{81 (u^{4} v^{20})}{81 (96 u^{22} v^{14})}$

Rewrite the expression.

$\frac{u^{4} v^{20}}{96 u^{22} v^{14}}$

Cancel the common factor of $u^{4}$ and $u^{22}$ .

Factor $u^{4}$ out of $u^{4} v^{20}$ .

$\frac{u^{4} (v^{20})}{96 u^{22} v^{14}}$

Cancel the common factors.

Factor $u^{4}$ out of $96 u^{22} v^{14}$ .

$\frac{u^{4} (v^{20})}{u^{4} (96 u^{18} v^{14})}$

Cancel the common factor.

$\frac{u^{4} v^{20}}{u^{4} (96 u^{18} v^{14})}$

Rewrite the expression.

$\frac{v^{20}}{96 u^{18} v^{14}}$

Cancel the common factor of $v^{20}$ and $v^{14}$ .

Factor $v^{14}$ out of $v^{20}$ .

$\frac{v^{14} v^{6}}{96 u^{18} v^{14}}$

Cancel the common factors.

Factor $v^{14}$ out of $96 u^{18} v^{14}$ .

$\frac{v^{14} v^{6}}{v^{14} (96 u^{18})}$

Cancel the common factor.

$\frac{v^{14} v^{6}}{v^{14} (96 u^{18})}$

Rewrite the expression.

$\frac{v^{6}}{96 u^{18}}$

Simplify ((u^4v^3)^-3(-3uv^5)^4)/((6u^2v)^5)

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