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Section 1.2 : Rational Exponents

3. Evaluate the following expression and write the answer as a single number without exponents.

\[ - {16^{\frac{3}{2}}}\]

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Hint : Don’t forget your basic exponent rules and how the first two practice problems worked. Also, be careful with minus signs in this problem.
Start Solution

First, let’s write the problem as,

\[ - \left( {{{16}^{\frac{3}{2}}}} \right)\]

so we aren’t tempted to bring the minus sign into the exponent.

Now, let’s recall our basic exponent rules and note that we can easily write this as,

\[ - \left( {{{16}^{\frac{3}{2}}}} \right) = - \left( {{{\left( {{{16}^{\frac{1}{2}}}} \right)}^3}} \right)\] Show Step 2

Now, recalling how the first two practice problems worked we can see that,

\[{16^{\frac{1}{2}}} = 4\]

because \({4^2} = 16\).


\[ - {16^{\frac{3}{2}}} = - \left( {{{16}^{\frac{3}{2}}}} \right) = - \left( {{{\left( {{{16}^{\frac{1}{2}}}} \right)}^3}} \right) = - \left( {{{\left( 4 \right)}^3}} \right) = - \left( {64} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 64}}\]

Sometimes the easiest way to do these kinds of problems when you first run into them is to break them up into manageable steps as we did here.