Select the correct answer to the following equation: x^ 5/4=243 .(1 point) Responses 27 27 no solution no solution 3 3 81

Answer 1

To solve the equation \( x^{5/4} = 243 \), we first isolate \( x \):

1. Rewrite the equation in terms of \( x \): \[ x = 243^{4/5} \]

2. Calculate \( 243 \): \[ 243 = 3^5 \]

3. Substitute \( 3^5 \) into the equation: \[ x = (3^5)^{4/5} \]

4. Use the power of a power property: \[ x = 3^{5 \cdot (4/5)} = 3^4 \]

5. Calculate \( 3^4 \): \[ 3^4 = 81 \]

Thus, the correct answer is: \[ \boxed{81} \]