Evaluate $2^{2-\log_{2}{5}}$

A special mathematical expression is given in this problem and we have to find the value of this expression.

$2^{\,\displaystyle 2-\log_{2}{5}}$

This mathematical expression is basically an expression in exponential form. The base of the term is $2$ but its exponent is an expression. It represents the subtraction of binary logarithm of five from two.

Express the expression in Rational form

$=\,\,\,$ $\dfrac{2^{\displaystyle 2}}{2^{\displaystyle \log_{2}{5}}}$

Evaluate the expression in the numerator

$=\,\,\,$ $\dfrac{2 \times 2}{2^{\displaystyle \log_{2}{5}}}$

$=\,\,\,$ $\dfrac{4}{2^{\displaystyle \log_{2}{5}}}$

Evaluate the expression in the denominator

$=\,\,\,$ $\dfrac{4}{5}$

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