Question

in this form, the exponent is a fraction. what do the two parts mean? 3. when a radical is written in exponential form, what does the numerator tell us? 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 fractional exponent \(x^{\frac{b}{a}}\), it can be written as a radical \(\sqrt[a]{x^{b}}\). The numerator \(b\) in the fraction \(\frac{b}{a}\) indicates the power to which the base \(x\) is raised. That is, we multiply the number \(x\) by itself \(b\) times.

Step2: Analyze the options

• Option A: The numerator \(b\) in the fractional exponent \(\frac{b}{a}\) tells us what to multiply the number by (i.e., multiply the base by itself \(b\) times).
• Option B: The denominator \(a\) in the fractional exponent \(\frac{b}{a}\) tells us the root (e.g., if \(a = 2\), it's a square - root; if \(a=3\), it's a cube - root).
• Option C: As mentioned above, the type of root is determined by the denominator of the fractional exponent.

Answer:

A. what to multiply the number by