which of the following is an equivalent expression to 81-^1/2?

Answer 1

To simplify the expression \( 81^{-1/2} \), you can use the properties of exponents.

The expression can be rewritten as follows:

\[ 81^{-1/2} = \frac{1}{81^{1/2}} \]

Next, we calculate \( 81^{1/2} \), which is the square root of 81:

\[ 81^{1/2} = \sqrt{81} = 9 \]

Therefore, substituting this back into the expression gives:

\[ 81^{-1/2} = \frac{1}{9} \]

So, the equivalent expression to \( 81^{-1/2} \) is:

\[ \frac{1}{9} \]

Answer 2

which of the following is an equivalent expression to 81-^1/2?

a. -sqrt81

b. 1/sqrt81

c. sqrt81

d. -1/sqrt81

Answer 3

Let's simplify the expression \( 81^{-1/2} \) again to find its equivalent expression.

1. Convert the exponent: \[ 81^{-1/2} = \frac{1}{81^{1/2}} \]

2. Calculate the square root: \[ 81^{1/2} = \sqrt{81} = 9 \]

3. Substituting back: \[ 81^{-1/2} = \frac{1}{9} \]

Now, we can compare \( 81^{-1/2} \) with the given options:

• \( a. -\sqrt{81} = -9 \)
• \( b. \frac{1}{\sqrt{81}} = \frac{1}{9} \)
• \( c. \sqrt{81} = 9 \)
• \( d. -\frac{1}{\sqrt{81}} = -\frac{1}{9} \)

The equivalent expression to \( 81^{-1/2} \) is:

b. \(\frac{1}{\sqrt{81}}\), which equals \(\frac{1}{9}\).