X3/5 write the expression in a radical form
The Correct Answer and Explanation is :
To express ( \frac{3}{5} ) as a radical, we aim to rewrite the expression in a form involving a radical symbol (square root, cube root, etc.). In this case, we’ll rewrite ( \frac{3}{5} ) using a radical for the exponent.
Step 1: Recall exponent rules
We know that ( a^b ) can be written as a radical as follows:
- ( a^b = \sqrt[b]{a} ), where ( a ) is the base and ( b ) is the exponent.
For ( \frac{3}{5} ), we recognize that this is a fractional exponent. We can rewrite it as:
[
\left( a^{\frac{3}{5}} \right) = \sqrt[5]{a^3}
]
Step 2: Applying to the given expression
For the expression ( \frac{3}{5} ), we apply the same principle. We can express it as a radical with the following steps:
[
\frac{3}{5} = 3^{\frac{3}{5}} = \sqrt[5]{3^3} = \sqrt[5]{27}
]
So, ( \frac{3}{5} ) written as a radical is ( \sqrt[5]{27} ).
Explanation of steps:
- Fractional Exponent Rule: We start by noting that a fractional exponent like ( \frac{m}{n} ) can be rewritten as ( a^{\frac{m}{n}} = \sqrt[n]{a^m} ).
- Apply the rule: For ( \frac{3}{5} ), this means the expression becomes ( 3^{\frac{3}{5}} ), which we convert into the radical form ( \sqrt[5]{3^3} ).
- Simplify the exponent: Since ( 3^3 = 27 ), the final result is ( \sqrt[5]{27} ).
Thus, the expression ( \frac{3}{5} ) in radical form is ( \sqrt[5]{27} ). This radical represents the fifth root of 27, which is the equivalent of taking ( 3^{\frac{3}{5}} ) in its fractional exponent form.
Conclusion:
In summary, expressing ( \frac{3}{5} ) as a radical involves rewriting the fractional exponent as a root. The expression ( 3^{\frac{3}{5}} ) becomes ( \sqrt[5]{27} ), which is the correct radical form of the given expression.