Find the numerical equivalent of 99⋅9−6 . Your answer should be written without exponents. (1 point) $$

Answer 1

To calculate $99\cdot 9^{-6}$, we first need to rewrite $9^{-6}$.

Using the definition of negative exponents, we have:

$$9^{-6}=\frac{1}{9^6}$$

Calculating $9^6$:

$$9^6=(3^2{)}^6=3^{12}$$

Calculating $3^{12}$:

1. First, calculate smaller powers:
   • $3^1=3$
   • $3^2=9$
   • $3^3=27$
   • $3^4=81$
   • $3^5=243$
   • $3^6=729$
   • $3^7=2187$
   • $3^8=6561$
   • $3^9=19683$
   • $3^{10}=59049$
   • $3^{11}=177147$
   • $3^{12}=531441$

Thus,

$$9^6=531441$$

Now plug this back into the expression for $9^{-6}$:

$$9^{-6}=\frac{1}{9^6}=\frac{1}{531441}$$

Now substitute this back into the original calculation:

$$99\cdot 9^{-6}=99\cdot \frac{1}{531441}=\frac{99}{531441}$$

Thus, the numerical equivalent of $99\cdot 9^{-6}$ is

$$\frac{99}{531441}$$

In decimal form, this value will be very small. However, if we need to find the answer without exponents in simple fraction form, it is:

$$\boxed{{\displaystyle \frac{99}{531441}}}$$