Question

1. evaluate the following expression, if possible.\\(25^{3/2}\\)\

select the correct choice below and fill in any answer boxes in your choice.\
\\(\bigcirc\\) a. \\(25^{3/2} = \square\\)\
\\(\bigcirc\\) b. the solution is not a real number.

Explanation:

Step1: Recall exponent rule

Recall that \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\) or \(a^{\frac{m}{n}} = (\sqrt[n]{a})^m\). For \(25^{\frac{3}{2}}\), we can use \(a^{\frac{m}{n}}=(\sqrt[n]{a})^m\) where \(a = 25\), \(n = 2\), \(m=3\).

Step2: Simplify the root first

First, find \(\sqrt{25}\). Since \(5\times5 = 25\), \(\sqrt{25}=5\).

Step3: Raise to the power of 3

Now, raise the result to the power of 3: \(5^3=5\times5\times5 = 125\).

Answer:

A. \(25^{\frac{3}{2}}=\boxed{125}\)