According to the exponent rules, what is the rational exponent in the equivalent expression to 5–√3

Question

? Enter your response in fraction form. (Hint: what should go in the yellow box)(1 point)
The rational exponent is

Answer 1

The expression \( 5\text{-}\sqrt{3} \) can be interpreted as \( 5 \) raised to the power of \( \frac{1}{\sqrt{3}} \).

Since the square root can be expressed as an exponent, we have:

\[ 5^{-\sqrt{3}} = 5^{-\frac{3}{2}} \text{ when rewritten correctly, depending on context.} \]

In this case, the rational exponent corresponding to \( 5\text{-}\sqrt{3} \) is \( -\frac{1}{2} \) if we treat it as a square root operation raising \( 5 \) to the negative half.

Thus, the rational exponent in fraction form is:

\[ -\frac{1}{2} \]