$\frac{ {3}^{4}{t}^{8} }{ {u}^{20} }$
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${\left( \frac{ 3{t}^{2} }{ {u}^{5} } \right)}^{4}$