Question

Simplify this equation 3 to the power of three times 3 to the power of negative two divided by (3 to the power of six) to the power of two

Answer 1

To simplify the equation \( \frac{3^3 \cdot 3^{-2}}{(3^6)^2} \), we will follow the rules of exponents.

First, simplify the numerator:

\[
3^3 \cdot 3^{-2} = 3^{3 + (-2)} = 3^{3 - 2} = 3^1 = 3
\]

Now, simplify the denominator:

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

Now, substitute the simplified numerator and denominator back into the expression:

\[
\frac{3^1}{3^{12}} = 3^{1 - 12} = 3^{-11}
\]

Finally, \( 3^{-11} \) can be expressed as:

\[
\frac{1}{3^{11}}
\]

So, the simplified form of the original equation is:

\[
\frac{1}{3^{11}}
\]