Find the numerical equivalent

Question

of . . Your answer
should be written without
exponents. (1 point)
9 ⋅
9 9
−6

Answer 1

To evaluate the expression \( 9 \cdot 9^{(-6)} \), we can start by simplifying it.

1. Recall that \( a^{-b} = \frac{1}{a^b} \). Therefore, we can rewrite \( 9^{-6} \) as: \[ 9^{-6} = \frac{1}{9^6} \]

2. Substitute this back into the expression: \[ 9 \cdot 9^{-6} = 9 \cdot \frac{1}{9^6} = \frac{9}{9^6} \]

3. Simplifying \( \frac{9}{9^6} \): \[ \frac{9}{9^6} = \frac{9^1}{9^6} = 9^{1-6} = 9^{-5} \]

4. Now, we can express \( 9^{-5} \) using the property of exponents: \[ 9^{-5} = \frac{1}{9^5} \]

5. Finally, we can calculate \( 9^5 \): \[ 9^5 = 9 \times 9 \times 9 \times 9 \times 9 = 59049 \]

6. Therefore, \[ \frac{1}{9^5} = \frac{1}{59049} \]

So, the numerical equivalent of \( 9 \cdot 9^{-6} \) is:

\[ \frac{1}{59049} \]

If you need the exact value expressed without fractions or exponents, it's:

0.0000161 (approximately)