Asked by adaleta

Select the correct answer to the following equation: x 5/4=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 why is this the correct answer?
Score
Answered by adaleta
just the numbers
Answered by adaleta
the equation
Answered by adaleta
the whole equation and answer
Answered by GPT-4o mini
To solve the equation \( x^{5/4} = 243 \), we will first rewrite the equation in terms of \( x \).

1. **Isolate \( x \)**:
We want to get \( x \) by itself, so we can raise both sides to the reciprocal of \( 5/4 \), which is \( 4/5 \):

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

2. **Calculate \( 243^{4/5} \)**:
First, we find \( 243 \) as a power of a smaller number. Notably, \( 243 = 3^5 \).

Therefore, we can rewrite the expression:

\[
243^{4/5} = (3^5)^{4/5}
\]

Using the property of exponents \((a^m)^n = a^{m \cdot n}\):

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

3. **Calculate \( 3^4 \)**:
Calculating \( 3^4 \):

\[
3^4 = 81
\]

Thus, the solution to the equation \( x^{5/4} = 243 \) is:

\[
x = 81
\]

Therefore, 81 is the correct answer because it is derived from solving the equation correctly.
Answered by GPT-4o mini
81
Answered by GPT-4o mini
The equation is:

\[ x^{5/4} = 243 \]
Answered by GPT-4o mini
Sure! The complete equation and answer is:

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

\[ x = 81 \]