Asked by hudson
Solve the following equation with a rational exponent: 5x43=80
.(1 point)
Responses
8
8
16
16
40.32
40.32
12
.(1 point)
Responses
8
8
16
16
40.32
40.32
12
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \( 5x^{43} = 80 \), we want to isolate \( x \).
1. First, divide both sides by 5:
\[
x^{43} = \frac{80}{5} = 16
\]
2. Now we have \( x^{43} = 16 \). To solve for \( x \), we take the 43rd root of both sides:
\[
x = 16^{\frac{1}{43}}
\]
3. We need to determine \( 16^{\frac{1}{43}} \). Since \( 16 = 2^4 \), we can rewrite it:
\[
x = (2^4)^{\frac{1}{43}} = 2^{\frac{4}{43}}
\]
Now, let's compare \( x = 2^{\frac{4}{43}} \) to the given choices. The answer \( 2^{\frac{4}{43}} \) is approximately \( 1.061\) when calculated, which does not match any of the provided options (8, 16, 40.32, 12).
Since none of the choices correctly reflect \( 2^{\frac{4}{43}} \), the answer can't be correctly selected from the options provided.
The correct approach concludes \( x = 2^{\frac{4}{43}} \).
1. First, divide both sides by 5:
\[
x^{43} = \frac{80}{5} = 16
\]
2. Now we have \( x^{43} = 16 \). To solve for \( x \), we take the 43rd root of both sides:
\[
x = 16^{\frac{1}{43}}
\]
3. We need to determine \( 16^{\frac{1}{43}} \). Since \( 16 = 2^4 \), we can rewrite it:
\[
x = (2^4)^{\frac{1}{43}} = 2^{\frac{4}{43}}
\]
Now, let's compare \( x = 2^{\frac{4}{43}} \) to the given choices. The answer \( 2^{\frac{4}{43}} \) is approximately \( 1.061\) when calculated, which does not match any of the provided options (8, 16, 40.32, 12).
Since none of the choices correctly reflect \( 2^{\frac{4}{43}} \), the answer can't be correctly selected from the options provided.
The correct approach concludes \( x = 2^{\frac{4}{43}} \).
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