Question

unit 2 quiz 2 study guide

1. what does it mean when an exponent is a fraction?

(for example: $4^{\frac{1}{2}}$)

Explanation:

A fractional exponent represents a root. For example, \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\). In the case of \(4^{\frac{1}{2}}\), the denominator \(n = 2\) (square root) and the numerator \(m=1\). So \(4^{\frac{1}{2}}=\sqrt{4}=2\).

Answer:

A fractional exponent \(a^{\frac{m}{n}}\) means taking the \(n\) - th root of \(a^{m}\). For \(4^{\frac{1}{2}}\), it means the square root of \(4\), and the value is \(2\).