Question

use the laws of exponents to generate an equivalent expression. what is the new value of the base? what is the new value of the exponent? 0 1/4 1/2 1 5/8

Explanation:

Step1: Recall exponent - division rule

When dividing two numbers with the same base \(a^m\div a^n=a^{m - n}\), here the base \(a = 364\), \(m=\frac{5}{2}\), and \(n=\frac{1}{2}\).
\[364^{\frac{5}{2}}\div364^{\frac{1}{2}}=364^{\frac{5}{2}-\frac{1}{2}}\]

Step2: Calculate the new exponent

\(\frac{5}{2}-\frac{1}{2}=\frac{5 - 1}{2}=\frac{4}{2}=2\)
So the new - value of the exponent is \(2\), and the new - value of the base is \(364\). The equivalent expression is \(364^2\).

Answer:

The new value of the exponent is \(2\), and the new value of the base is \(364\).