Question

According to exponent rules, what is the rational exponent in the equivalent expression to 5√3
? Enter your response in fraction form.(1 point)

Answer 1

the answers 12?

Answer 2

According to exponent rules, what is the rational exponent in the equivalent expression to 3√5
? Enter your response in fraction form.(1 point)

Answer 3

The expression \( 5\sqrt{3} \) can be rewritten using exponent rules. The square root can be expressed as an exponent of \( \frac{1}{2} \). Therefore, we can express the square root as follows:

\[ \sqrt{3} = 3^{\frac{1}{2}} \]

So, \( 5\sqrt{3} \) can be rewritten as:

\[ 5 \cdot 3^{\frac{1}{2}} \]

The rational exponent for the square root of 3 in this expression is \( \frac{1}{2} \). Therefore, the answer is:

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

Answer 4

It seems there might have been a mix-up in interpreting your question regarding \( 5\sqrt{3} \). The expression \( 5\sqrt{3} \) involves the square root of 3 multiplied by 5, and the exponent associated with the square root of 3 is \( \frac{1}{2} \).

However, if you are asking for a different element of the expression that yields 12, please clarify further.

To clarify:

- The rational exponent for \( \sqrt{3} \) is indeed \( \frac{1}{2} \).
- If you are referring to finding the value of \( 5\sqrt{3} \), that would be \( 5 \times \sqrt{3} \), which is approximately \( 8.660 \) when \( \sqrt{3} \) is evaluated.

Please let me know if you would like additional information or if there is another concept you are referring to!

Answer 5

The expression \( \sqrt[3]{5} \) (which is the cube root of 5) can be expressed using a rational exponent. According to the rules of exponents, the cube root can be written as a power of \( \frac{1}{3} \).

Thus, we can write:

\[
\sqrt[3]{5} = 5^{\frac{1}{3}}
\]

So, the rational exponent in the equivalent expression to \( \sqrt[3]{5} \) is:

\[
\frac{1}{3}
\]