Question

Select the correct answer to the following equation: x54=243
.
Responses

3
3 - incorrect

27
27 - no response given

no solution
no solution - no response given

81
81 - not selected, this is the correct answer
Score tell me how this is correct and just with number

Answer 1

Select the correct answer to the following equation: x5/4=243

3
3 - incorrect

27
27 - no response given

no solution
no solution - no response given

81 this is the correct answer tell me why?


.

Answer 2

The correct answer is 81.

Here's why:

The equation is \( x54 = 243 \).

To solve for \( x \), you isolate \( x \):

1. Divide both sides of the equation by 54:
\[ x = \frac{243}{54} \]

2. Calculate \( \frac{243}{54} \):
\[ \frac{243}{54} = 4.5 \]

Since you mentioned "this is the correct answer" is 81, it seems there might have been a misunderstanding in the initial question or response.

If you are looking for a power expression like \( x^3 = 243 \), that would indeed lead you to \( x = 3 \), because \( 3^3 = 27 \), but \( 3^5 = 243 \) would yield \( x = 3 \) as well.

If you need clarification or if there's a specific reinterpretation of "x54" you'd like to elaborate on, please let me know! Otherwise, based on the division provided, the correct simplistic answer is \( 4.5 \).

Answer 3

To solve the equation \( x^{5/4} = 243 \), we need to isolate \( x \). Here's how you do it step by step:

1. **Raise both sides to the power of the reciprocal of \( \frac{5}{4} \)**, which is \( \frac{4}{5} \):

\[
x = 243^{\frac{4}{5}}
\]

2. **Calculate \( 243^{\frac{4}{5}} \)**:

First, remember that \( 243 = 3^5 \). Therefore, we can rewrite the expression as:

\[
x = (3^5)^{\frac{4}{5}} = 3^{5 \cdot \frac{4}{5}} = 3^4
\]

3. **Compute \( 3^4 \)**:

\[
3^4 = 81
\]

So, the correct answer is indeed \( x = 81 \).

Therefore, the response is:

**81 is the correct answer because solving \( x^{5/4} = 243 \) leads to \( x = 243^{4/5} = 3^4 = 81 \).**