Question

If ${20}^{-x}=\frac{1}{7}$ then find the value of ${20}^{2x}$.

Answer 1

${20}^{-x}=\frac{1}{7}$
Squaring both sides, we get,
${\left({20}^{-x}\right)}^2={\left(\frac{1}{7}\right)}^2\Rightarrow \left({20}^{-2x}\right)=\frac{1}{49}\Rightarrow \frac{1}{{20}^{2x}}=\frac{1}{49}\Rightarrow {20}^{2x}=49$
Hence the required value is 49.