Question

What rational number could be used as an exponent to rewrite 82−−√3
8
2
3
? Then, simplify the expression. (2 points)
The rational number that could be used as an exponent is

Answer 1

To rewrite \( \sqrt[3]{82} \) using an exponent, we can express it in terms of fractional exponents:

\[
\sqrt[3]{82} = 82^{1/3}
\]

Now, we can simplify the expression \( 82^{1/3} \).

Thus, the rational number that could be used as an exponent is \( \frac{1}{3} \).

So, to summarize:

- The rational number that could be used as an exponent is \( \frac{1}{3} \).
- The simplified expression is \( 82^{1/3} \).