Question

Using the properties of exponents, which of the following is an equivalent expression for square root 25/25 1/2?

1/5
5^0
5
1

Answer 1

To simplify the expression \(\sqrt{\frac{25}{25}}^{1/2}\), we can use the properties of exponents and the fact that the square root can be expressed as a fractional exponent.

First, simplify \(\frac{25}{25}\):

\[
\frac{25}{25} = 1
\]

Taking the square root (which is equivalent to raising to the 1/2 power) of \(1\):

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

Since any number raised to the power of 1/2 is still the same number, we have:

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

So, the equivalent expression for \(\sqrt{\frac{25}{25}}^{1/2}\) is:

\[
1
\]

Thus, the answer is:

**1**