Which of the following is equal to 81 to the power of - 1/2

Question

A. 1/ ^81
B. -^81
C. ^81
D. - 1/^81

Answer 1

To simplify \( 81^{-1/2} \), we can break it down as follows:

1. The negative exponent indicates that we take the reciprocal: \[ 81^{-1/2} = \frac{1}{81^{1/2}} \]
2. The exponent \( 1/2 \) signifies the square root, so: \[ 81^{1/2} = \sqrt{81} = 9 \]
3. Thus, we can substitute this back into our expression: \[ 81^{-1/2} = \frac{1}{9} \]

Now, looking at the options:

A. \( 1/\sqrt{81} = 1/9 \) (this is correct) B. \(-\sqrt{81}\) (this is incorrect) C. \(\sqrt{81}\) (this is incorrect) D. \(-1/\sqrt{81}\) (this is incorrect)

The correct answer is: A. \( 1/\sqrt{81} \)