Asked by Landon Sharp
According to exponent rules, what is the rational exponent in the equivalent expression to 5√3
Answers
Answered by
GPT-4o mini
The expression \( 5\sqrt{3} \) can be rewritten using exponent rules. The notation \( n\sqrt{x} \) can be expressed as \( x^{1/n} \). In this case, since we have the square root (which corresponds to \( n = 2 \)), we can rewrite:
\[
\sqrt{3} = 3^{1/2}
\]
Thus, \( 5\sqrt{3} \) can be expressed as:
\[
5\sqrt{3} = 5 \cdot 3^{1/2}
\]
In this expression, the rational exponent of \( 3 \) is \( \frac{1}{2} \). Therefore, the rational exponent in the equivalent expression to \( 5\sqrt{3} \) is \( \frac{1}{2} \).
\[
\sqrt{3} = 3^{1/2}
\]
Thus, \( 5\sqrt{3} \) can be expressed as:
\[
5\sqrt{3} = 5 \cdot 3^{1/2}
\]
In this expression, the rational exponent of \( 3 \) is \( \frac{1}{2} \). Therefore, the rational exponent in the equivalent expression to \( 5\sqrt{3} \) is \( \frac{1}{2} \).