Find the numerical equivalent of 99⋅9−6

Question

. Your answer should be written without exponents.

Answer 1

To find the numerical equivalent of \( 99 \cdot 9^{-6} \), we can first evaluate \( 9^{-6} \).

Recall that \( 9^{-6} \) means \( \frac{1}{9^6} \). We can calculate \( 9^6 \) as follows:

\[ 9 = 3^2 \] \[ 9^6 = (3^2)^6 = 3^{12} \]

Now, we need to find \( 3^{12} \): \[ 3^{12} = 531441 \]

Thus, we have: \[ 9^{-6} = \frac{1}{9^6} = \frac{1}{531441} \]

Now, we can substitute this back into our original expression: \[ 99 \cdot 9^{-6} = 99 \cdot \frac{1}{531441} = \frac{99}{531441} \]

Therefore, the numerical equivalent of \( 99 \cdot 9^{-6} \) is: \[ \frac{99}{531441} \]

To express this without exponents: \[ \frac{99}{531441} \]

This fraction is already in a simplified form, so the final answer is: \[ \frac{99}{531441} \]