Question

Use the properties of exponents to generate an equivalent expression for 3 radical 8 / radical 2
.(1 point)
$$

Answer 1

To simplify the expression \( \frac{3 \sqrt{8}}{\sqrt{2}} \) using properties of exponents and radicals, we can start by rewriting the square roots as exponents.

We know that:
\[
\sqrt{a} = a^{1/2}
\]
Thus, we can rewrite the expression as:
\[
\frac{3 \sqrt{8}}{\sqrt{2}} = \frac{3 \cdot 8^{1/2}}{2^{1/2}}
\]

Using the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \), we can rewrite the expression:
\[
\frac{8^{1/2}}{2^{1/2}} = ( \frac{8}{2} )^{1/2}
\]

Now, simplify \( \frac{8}{2} = 4 \):
\[
\frac{3 \sqrt{8}}{\sqrt{2}} = 3 \cdot (4^{1/2}) = 3 \cdot 2
\]

Thus, we have:
\[
3 \cdot 2 = 6
\]

So the equivalent expression for \( \frac{3 \sqrt{8}}{\sqrt{2}} \) is:
\[
6
\]

Therefore, the final answer is \( \boxed{6} \).