To evaluate the expressions \( 9^{1/2} \) and \( 9^{1/6} \), we start by rewriting the base.
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Calculate \( 9^{1/2} \): \[ 9^{1/2} = \sqrt{9} = 3 \]
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Calculate \( 9^{1/6} \): First, we can express \( 9 \) as \( 3^2 \): \[ 9^{1/6} = (3^2)^{1/6} = 3^{2/6} = 3^{1/3} \] Now, we can compute \( 3^{1/3} \), which is the cube root of 3. Thus, the result is approximately: \[ 3^{1/3} \approx 1.442 \]
In summary:
- \( 9^{1/2} = 3 \)
- \( 9^{1/6} \approx 1.442 \) (which is \( 3^{1/3} \))