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Question

# Simplify the expression.$13 ^ { \frac { 1 } { 2 } } \cdot 13 ^ { \frac { 3 } { 2 } }$

Solution

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Step 1
1 of 2

Remember:

\begin{align*}{\color{#965501}a^b\cdot a^c=a^{b+c}} \tag{Product of Powers Property}\end{align*}

Now, use property above (for $a=13$, $b=\dfrac{1}{2}$ and $c=\dfrac{3}{2}$) to transform given expression to:

\begin{align*} 13^{\tfrac{1}{2}+\tfrac{3}{2}}&=13^{\tfrac{1+3}{2}}\tag{Add fractions in exponent}\\ &=13^{\tfrac{4}{2}}\\ &=13^{2}\\ &=\boxed{169} \end{align*}

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