Question

13^-9*13*13^-5 fully simplify and write your answer in exponential form with positive exponents only.

Answer 1

To simplify the expression \( 13^{-9} \cdot 13 \cdot 13^{-5} \), we can use the properties of exponents. Specifically, we can use the rule that states \( a^m \cdot a^n = a^{m+n} \).

First, we rewrite \( 13 \) as \( 13^1 \):

\[
13^{-9} \cdot 13^1 \cdot 13^{-5}
\]

Now we can add the exponents together:

\[
-9 + 1 - 5
\]

Calculating this:

\[
-9 + 1 = -8
\]
\[
-8 - 5 = -13
\]

This gives us:

\[
13^{-13}
\]

To write this in exponential form with a positive exponent, we can use the property \( a^{-m} = \frac{1}{a^m} \):

\[
13^{-13} = \frac{1}{13^{13}}
\]

Thus, the fully simplified expression in exponential form with positive exponents is:

\[
\frac{1}{13^{13}}
\]