Question
what rational exponent could be used to express 4√23?
the denominator of the rational exponent should match the type of root. what will the numerator be?
the denominator of the rational exponent should match the type of root. what will the numerator be?
Answers
GPT-4o mini
To express \( 4\sqrt{23} \) using a rational exponent, we can first identify that the expression represents the fourth root of 23. In terms of exponents, the fourth root can be expressed as raising to the power of \( \frac{1}{4} \).
Thus, we can represent \( 4\sqrt{23} \) as:
\[
23^{\frac{1}{4}}
\]
In this case, the denominator of the rational exponent is \( 4 \) because we are taking the fourth root.
For the numerator, since we do not have any other factors multiplying the \( 4\sqrt{23} \) (it is simply the fourth root of \( 23 \)), the numerator will be \( 1 \).
Therefore, the rational exponent that can be used to express \( 4\sqrt{23} \) is:
\[
\frac{1}{4}
\]
In summary:
- The denominator is \( 4 \).
- The numerator is \( 1 \), so the rational exponent is \( 23^{\frac{1}{4}} \).
Thus, we can represent \( 4\sqrt{23} \) as:
\[
23^{\frac{1}{4}}
\]
In this case, the denominator of the rational exponent is \( 4 \) because we are taking the fourth root.
For the numerator, since we do not have any other factors multiplying the \( 4\sqrt{23} \) (it is simply the fourth root of \( 23 \)), the numerator will be \( 1 \).
Therefore, the rational exponent that can be used to express \( 4\sqrt{23} \) is:
\[
\frac{1}{4}
\]
In summary:
- The denominator is \( 4 \).
- The numerator is \( 1 \), so the rational exponent is \( 23^{\frac{1}{4}} \).