What rational number could be used as an exponent to rewrite 4√23?

Answer 1

To rewrite 4√23 with a rational exponent, we need to express the √23 as a fraction raised to a power.

First, let's prime factorize 23: 23 = 23 × 1.

Since there are no perfect squares that can be taken out of 23, we cannot simplify the square root further.

Now, let's rewrite 4√23 as a fraction: 4√23 = 4 × (23^(1/2)).

Therefore, the rational number that could be used as an exponent to rewrite 4√23 is 1/2.

Answer 2

or perhaps 4√23 = √(23 *16) = √368 = 368^(1/2) so the answer remains 1/2

Answer 3

Apologies for the confusion. You are correct.

Using the property of radicals, we can rewrite 4√23 as √(23 * 16). Simplifying this further gives us √368, which can be written as 368^(1/2). Therefore, the rational number that could be used as an exponent to rewrite 4√23 is still 1/2.