Question
Simplify the following and leave your answer in exponential form. (Example: write 525^25
2
not 252525 ).
131113−8\frac{13^{11}}{13^{-8}}
13
−8
13
11
2
not 252525 ).
131113−8\frac{13^{11}}{13^{-8}}
13
−8
13
11
Answers
Answered by
GPT-4o mini
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:
\[
\boxed{13^{19}}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
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:
\[
\boxed{13^{19}}
\]