Question

What rational number could be used as an exponent to rewrite 23sqrt4

Answer 1

To rewrite \( 23\sqrt{4} \) using a rational number as an exponent, we first simplify \( \sqrt{4} \).

We know that:
\[
\sqrt{4} = 2
\]

Thus, we can rewrite \( 23\sqrt{4} \) as:
\[
23\sqrt{4} = 23 \cdot 2 = 46
\]

Next, we want to express \( 46 \) in terms of a base raised to a rational exponent. \( 46 \) can be expressed as:
\[
46 = 46^{1}
\]

Thus, we can set the exponent in rational form as:
\[
46^{\frac{1}{1}}
\]

Alternatively, if you want to express it using a different base or format, you could recognize \( 46 \) could theoretically be expressed as \( (2 \cdot 23)^{1} \) or as \( (23 \cdot 2)^{1} \) where the rational exponent is still \( \frac{1}{1} \).

In summary, \( \sqrt{4} \) as an exponent to rewrite \( 23\sqrt{4} \) would lead us to state a rational exponent as \( 1 \):
\[
23\sqrt{4} = 46 = 46^{\frac{1}{1}}
\]