Simplify the following and leave your answer in exponential form. (Example: write 525^25

Question

2
not 252525 ).

131113−8\frac{13^{11}}{13^{-8}}
13
−8

13
11

​

Answer 1

To simplify the expression \(\frac{13^{11}}{13^{-8}}\), we can use the properties of exponents. Specifically, we can apply the rule:

\[ \frac{a^m}{a^n} = a^{m-n} \]

In this case, we have:

\[ m = 11 \quad \text{and} \quad n = -8 \]

So we can simplify the expression as follows:

\[ \frac{13^{11}}{13^{-8}} = 13^{11 - (-8)} = 13^{11 + 8} = 13^{19} \]

Thus, the simplified expression is:

\[ \boxed{13^{19}} \]