Question

Simplified expression
5^1/3 • 5^1/6

Answer 1

To simplify the expression \( 5^{1/3} \cdot 5^{1/6} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Here, we have:

\[
5^{1/3} \cdot 5^{1/6} = 5^{(1/3 + 1/6)}
\]

Next, we need to add the exponents \( \frac{1}{3} \) and \( \frac{1}{6} \). To do this, we'll find a common denominator. The least common multiple of 3 and 6 is 6.

Convert \( \frac{1}{3} \) to have a denominator of 6:

\[
\frac{1}{3} = \frac{2}{6}
\]

Now, add \( \frac{2}{6} \) and \( \frac{1}{6} \):

\[
\frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}
\]

Now we can simplify the expression:

\[
5^{1/3} \cdot 5^{1/6} = 5^{1/2}
\]

Thus, the simplified expression is:

\[
5^{1/2} = \sqrt{5}
\]

So, the final answer is:

\[
\sqrt{5}
\]