Question

3.when a radical is written in exponential form, what does the numerator tell us? in this form, the exponent is a fraction. what do the two parts mean? a what to multiply the number by b how many times to multiply the number by itself c what type of root it is

Explanation:

Step1: Recall the rule of fractional exponents

For a radical in exponential form \(x^{\frac{b}{a}}\), it can be written as \(\sqrt[a]{x^{b}}\). The numerator \(b\) of the fraction exponent represents the power of the base \(x\), that is, what to multiply the number by itself \(b\) times.

Step2: Analyze each option

• Option A: The numerator \(b\) in the fraction exponent \(\frac{b}{a}\) tells us what to multiply the number by itself. For example, if we have \(x^{\frac{2}{3}}\), the numerator \(2\) means we first square the base \(x\) (multiply \(x\) by itself \(2\) times).
• Option B: The denominator \(a\) of the fraction exponent \(\frac{b}{a}\) tells us the root. For \(x^{\frac{b}{a}}=\sqrt[a]{x^{b}}\), the \(a\) represents the \(a\) - th root.
• Option C: As mentioned above, it is the denominator that tells us the type of root.

Answer:

A. what to multiply the number by