Questions: Write this expression with a positive exponent and then simplify. 9^(-2) =

Write this expression with a positive exponent and then simplify. 9^(-2) =
Transcript text: Write this expression with a positive exponent and then simplify. $9^{-2}=$ $\square$
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Solution

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Solution Steps

To rewrite the expression with a positive exponent, we use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \). Therefore, \( 9^{-2} \) can be rewritten as \( \frac{1}{9^2} \). Then, we simplify by calculating \( 9^2 \).

Step 1: Rewrite the Expression

We start with the expression \( 9^{-2} \). To express this with a positive exponent, we use the property of exponents:

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

Step 2: Calculate \( 9^2 \)

Next, we calculate \( 9^2 \):

\[ 9^2 = 81 \]

Step 3: Simplify the Expression

Now, substituting back into our expression, we have:

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

Final Answer

Thus, the simplified expression with a positive exponent is

\[ \boxed{\frac{1}{81}} \]

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