Select the correct answer to the following equation: x

Question

5
4

=243.(1 point)
Responses

3
3

no solution
no solution

27
27

81

Answer 1

To solve the equation \( x^{\frac{5}{4}} = 243 \), we need to isolate \( x \).

1. Start by raising both sides to the power of \( \frac{4}{5} \) to eliminate the exponent on \( x \): \[ x = 243^{\frac{4}{5}} \]

2. Next, we can simplify \( 243 \). We know that \( 243 = 3^5 \).

3. Substituting this in gives: \[ x = (3^5)^{\frac{4}{5}} = 3^{5 \cdot \frac{4}{5}} = 3^4 \]

4. We calculate \( 3^4 \): \[ 3^4 = 81 \]

So, the correct answer is:

81