Question
Solve the following equation with a rational exponent: 2x3/2=16
.(1 point)
Responses
4
4
84
84
8
8
no solution
.(1 point)
Responses
4
4
84
84
8
8
no solution
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \(2x^{3/2} = 16\), follow these steps:
1. Divide both sides by 2:
\[
x^{3/2} = \frac{16}{2} = 8
\]
2. Now, to eliminate the rational exponent, raise both sides to the power of \(\frac{2}{3}\):
\[
x = 8^{\frac{2}{3}}
\]
3. Calculate \(8^{\frac{2}{3}}\). First, find \(8^{\frac{1}{3}}\), which is the cube root of 8:
\[
8^{\frac{1}{3}} = 2
\]
4. Now, square the result:
\[
(8^{\frac{1}{3}})^2 = 2^2 = 4
\]
Thus, the solution to the equation \(2x^{3/2} = 16\) is \(x = 4\).
The correct response is **4**.
1. Divide both sides by 2:
\[
x^{3/2} = \frac{16}{2} = 8
\]
2. Now, to eliminate the rational exponent, raise both sides to the power of \(\frac{2}{3}\):
\[
x = 8^{\frac{2}{3}}
\]
3. Calculate \(8^{\frac{2}{3}}\). First, find \(8^{\frac{1}{3}}\), which is the cube root of 8:
\[
8^{\frac{1}{3}} = 2
\]
4. Now, square the result:
\[
(8^{\frac{1}{3}})^2 = 2^2 = 4
\]
Thus, the solution to the equation \(2x^{3/2} = 16\) is \(x = 4\).
The correct response is **4**.
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