College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.3 - Page 51: 141


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.
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