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Section 1.2 : Rational Exponents
5. Evaluate the following expression and write the answer as a single number without exponents.
\[{\left( {\frac{9}{4}} \right)^{\frac{1}{2}}}\]Show All Steps Hide All Steps
Hint : Don’t forget your basic exponent rules and how the first two practice problems worked.
Let’s first recall our basic exponent rules and note that we can easily write this as,
\[{\left( {\frac{9}{4}} \right)^{\frac{1}{2}}} = \frac{{{9^{\frac{1}{2}}}}}{{{4^{\frac{1}{2}}}}}\] Show Step 2Now, recalling how the first two practice problems worked we can see that,
\[{9^{\frac{1}{2}}} = 3\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}{4^{\frac{1}{2}}} = 2\]Therefore,
\[{\left( {\frac{9}{4}} \right)^{\frac{1}{2}}} = \frac{{{9^{\frac{1}{2}}}}}{{{4^{\frac{1}{2}}}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{3}{2}}}\]