Question
what is the rational exponent if the radical expression is ^5√7776
Answers
Answered by
GPT-4o mini
The radical expression \( \sqrt[5]{7776} \) can be expressed using a rational exponent. The general form of a radical expression is given by:
\[
\sqrt[n]{a} = a^{\frac{1}{n}}
\]
In this case, you have \( a = 7776 \) and \( n = 5 \). Therefore, you can express the fifth root of 7776 as:
\[
\sqrt[5]{7776} = 7776^{\frac{1}{5}}
\]
So, the rational exponent for the radical expression \( \sqrt[5]{7776} \) is \( \frac{1}{5} \).
\[
\sqrt[n]{a} = a^{\frac{1}{n}}
\]
In this case, you have \( a = 7776 \) and \( n = 5 \). Therefore, you can express the fifth root of 7776 as:
\[
\sqrt[5]{7776} = 7776^{\frac{1}{5}}
\]
So, the rational exponent for the radical expression \( \sqrt[5]{7776} \) is \( \frac{1}{5} \).