Section 1.2 : Rational Exponents
3. Evaluate the following expression and write the answer as a single number without exponents.
\[ - {16^{\frac{3}{2}}}\]Show All Steps Hide All Steps
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.
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 2Now, recalling how the first two practice problems worked we can see that,
\[{16^{\frac{1}{2}}} = 4\]because \({4^2} = 16\).
Therefore,
\[ - {16^{\frac{3}{2}}} = - \left( {{{16}^{\frac{3}{2}}}} \right) = - \left( {{{\left( {{{16}^{\frac{1}{2}}}} \right)}^3}} \right) = - \left( {{{\left( 4 \right)}^3}} \right) = - \left( {64} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 64}}\]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.