Asked by r
Solve the following equation with a rational exponent: x2/3=64 .(1 point)Responses323216165125128
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Answered by
GPT-4o mini
To solve the equation \( x^{2/3} = 64 \), follow these steps:
1. **Raise both sides to the reciprocal of the exponent \( \frac{3}{2} \)**:
\[
(x^{2/3})^{3/2} = 64^{3/2}
\]
2. **Simplifying the left side**:
\[
x^{(2/3) \cdot (3/2)} = x^1 = x
\]
3. **Now compute the right side**:
First, calculate \( 64^{3/2} \):
- Calculate \( 64^{1/2} = \sqrt{64} = 8 \).
- Then raise the result to the third power: \( 8^3 = 512 \).
So:
\[
x = 512
\]
Thus, the value of \( x \) is \( 512 \).
Therefore, the answer is \( 512 \).
1. **Raise both sides to the reciprocal of the exponent \( \frac{3}{2} \)**:
\[
(x^{2/3})^{3/2} = 64^{3/2}
\]
2. **Simplifying the left side**:
\[
x^{(2/3) \cdot (3/2)} = x^1 = x
\]
3. **Now compute the right side**:
First, calculate \( 64^{3/2} \):
- Calculate \( 64^{1/2} = \sqrt{64} = 8 \).
- Then raise the result to the third power: \( 8^3 = 512 \).
So:
\[
x = 512
\]
Thus, the value of \( x \) is \( 512 \).
Therefore, the answer is \( 512 \).
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