Question

Find the numerical equivalent of 3 to the ninth power times 3 to the negative fifth power

Answer 1

To solve \( 3^9 \times 3^{-5} \), we can utilize the property of exponents which states that when multiplying like bases, we can add the exponents:

\[
a^m \times a^n = a^{m+n}
\]

Applying this to our problem:

\[
3^9 \times 3^{-5} = 3^{9 + (-5)} = 3^{9 - 5} = 3^4
\]

Next, we need to calculate \( 3^4 \):

\[
3^4 = 3 \times 3 \times 3 \times 3
\]

Calculating step-by-step:

\[
3 \times 3 = 9
\]
\[
9 \times 3 = 27
\]
\[
27 \times 3 = 81
\]

Thus, \( 3^4 = 81 \).

Therefore, the numerical equivalent of \( 3^9 \times 3^{-5} \) is

\[
\boxed{81}
\]