Calculate: ((x^5y^{10})/(4))^3 * ((x^4y^{30})/(4^2))^{-1}

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  3. Calculate: ((x^5y^{10})/(4))^3 * ((x^4y^{30})/(4^2))^{-1}

Expression: ${\left( \frac{ {x}^{5}{y}^{10} }{ 4 } \right)}^{3} \times {\left( \frac{ {x}^{4}{y}^{30} }{ {4}^{2} } \right)}^{-1}$

To raise a fraction to a power, raise the numerator and denominator to that power

$\frac{ {x}^{15}{y}^{30} }{ 64 } \times {\left( \frac{ {x}^{4}{y}^{30} }{ {4}^{2} } \right)}^{-1}$

Any expression raised to the power of $-1$ equals its reciprocal

$\frac{ {x}^{15}{y}^{30} }{ 64 } \times \frac{ {4}^{2} }{ {x}^{4}{y}^{30} }$

Write the number in exponential form with the base of $4$

$\frac{ {x}^{15}{y}^{30} }{ {4}^{3} } \times \frac{ {4}^{2} }{ {x}^{4}{y}^{30} }$

Cancel out the common factor ${y}^{30}$

$\frac{ {x}^{15} }{ {4}^{3} } \times \frac{ {4}^{2} }{ {x}^{4} }$

Cancel out the common factor ${x}^{4}$

$\frac{ {x}^{11} }{ {4}^{3} } \times {4}^{2}$

Cancel out the common factor ${4}^{2}$

$\frac{ {x}^{11} }{ 4 }$

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