Question

Radicals and radicals exponents quick check which of the following is an equivalent expression for 5 and 1/2 over three square root 125 when simplified using exponent properties square root 5 over 5 1 5 with power of zero one is it

Answer 1

To find an equivalent expression for \(\frac{5^{1/2}}{3\sqrt{125}}\), we will simplify the expression step by step using exponent properties and radical rules.

1. **Simplify \(\sqrt{125}\) first:**
\[
\sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt{5}
\]

2. **Now substitute \(\sqrt{125}\) back into the expression:**
\[
\frac{5^{1/2}}{3\sqrt{125}} = \frac{5^{1/2}}{3(5\sqrt{5})}
\]

3. **Combine the terms in the denominator:**
\[
= \frac{5^{1/2}}{15\sqrt{5}}
\]

4. **Rewrite \(\sqrt{5}\) as \(5^{1/2}\):**
\[
= \frac{5^{1/2}}{15 \cdot 5^{1/2}}
\]

5. **Now, cancel \(5^{1/2}\) in the numerator and denominator:**
\[
= \frac{1}{15}
\]

Thus, the simplified expression is \(\frac{1}{15}\).

Now, let’s compare this with the given options:

- Square root 5 over 5: \(\frac{\sqrt{5}}{5}\)
- 1: \(1\)
- 5 with power of zero: \(5^0 = 1\)

Since we found the simplified expression to be \(\frac{1}{15}\), none of the options given (\(\sqrt{5}/5\), \(1\), \(5^0\)) are equivalent to our simplified result.

Hence, none of the provided options are correct. If there are additional options you wish to check, please provide them.