Answer
8 years old
Work Step by Step
$$2^{\frac{5}{2}} \times 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}$$ Since the three numbers have the same base ($2$), we can use the properties of exponents to combine them as follows: $$2^{\frac{5}{2} + \frac{3}{4} - \frac{1}{4}}$$ Focusing on the fractions for a moment, we only have to find the common denominator ($4$) to solve the expression:
$$(\frac{5}{2} \times \frac{2}{2}) + \frac{3}{4} - \frac{1}{4}$$ $= \frac{10}{4} + \frac{3}{4} - \frac{1}{4}$
$= \frac{12}{4}$
$=3$
Therefore, the answer is $2^3 = 8$ years old.
