# Solve for: (81t^8)/(u^{20)}

## Expression: $\frac{ 81{t}^{8} }{ {u}^{20} }$

Write the number in exponential form with the base of $3$

$\frac{ {3}^{4}{t}^{8} }{ {u}^{20} }$

Write the number as a product with the factor $4$

$\frac{ {3}^{4}{t}^{4 \times 2} }{ {u}^{20} }$

Write the number as a product with the factor $4$

$\frac{ {3}^{4}{t}^{4 \times 2} }{ {u}^{4 \times 5} }$

Use ${a}^{mn}={\left( {a}^{n} \right)}^{m}$ to transform the expression

$\frac{ {3}^{4} \times {\left( {t}^{2} \right)}^{4} }{ {u}^{4 \times 5} }$

Use ${a}^{mn}={\left( {a}^{n} \right)}^{m}$ to transform the expression

$\frac{ {3}^{4} \times {\left( {t}^{2} \right)}^{4} }{ {\left( {u}^{5} \right)}^{4} }$

Multiply the terms with equal exponents by multiplying their bases

$\frac{ {\left( 3{t}^{2} \right)}^{4} }{ {\left( {u}^{5} \right)}^{4} }$

Simplify the expression by multiplying exponents

$\frac{ {\left( 3{t}^{2} \right)}^{4} }{ {u}^{20} }$

Write the number as a product with the factor $4$

$\frac{ {\left( 3{t}^{2} \right)}^{4} }{ {u}^{4 \times 5} }$

Use ${a}^{mn}={\left( {a}^{n} \right)}^{m}$ to transform the expression

$\frac{ {\left( 3{t}^{2} \right)}^{4} }{ {\left( {u}^{5} \right)}^{4} }$

When the numerator and denominator are raised to the same power, raise the whole fraction to that power

${\left( \frac{ 3{t}^{2} }{ {u}^{5} } \right)}^{4}$

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