# Calculate: (5^0)/(5^{-6)} * (1)/(5^{-11)}/((5^2)^4)/((5^{10))^2}

## Expression: $\frac{ {5}^{0} }{ {5}^{-6} } \times \frac{ 1 }{ {5}^{-11} }\div\frac{ {\left( {5}^{2} \right)}^{4} }{ {\left( {5}^{10} \right)}^{2} }$

Any non-zero expression raised to the power of $0$ equals $1$

$\frac{ 1 }{ {5}^{-6} } \times \frac{ 1 }{ {5}^{-11} }\div\frac{ {\left( {5}^{2} \right)}^{4} }{ {\left( {5}^{10} \right)}^{2} }$

Simplify the expression by multiplying exponents

$\frac{ 1 }{ {5}^{-6} } \times \frac{ 1 }{ {5}^{-11} }\div\frac{ {5}^{8} }{ {\left( {5}^{10} \right)}^{2} }$

Simplify the expression by multiplying exponents

$\frac{ 1 }{ {5}^{-6} } \times \frac{ 1 }{ {5}^{-11} }\div\frac{ {5}^{8} }{ {5}^{20} }$

To divide by a fraction, multiply by the reciprocal of that fraction

$\frac{ 1 }{ {5}^{-6} } \times \frac{ 1 }{ {5}^{-11} } \times \frac{ {5}^{20} }{ {5}^{8} }$

Simplify the expression

$\frac{ 1 }{ {5}^{-6} } \times \frac{ 1 }{ {5}^{-11} } \times {5}^{12}$

Cancel out the common factor ${5}^{-6}$

$\frac{ 1 }{ {5}^{-11} } \times {5}^{18}$

Cancel out the common factor ${5}^{-11}$

\begin{align*}&{5}^{29} \\&\approx1.86265 \times {10}^{20}\end{align*}

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