Question
Simplify 13 with an exponent of 12 divided by 13 with an exponent of -10.
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{13^{12}}{13^{-10}} \), we use the rule of exponents which states that when dividing like bases, we subtract the exponents:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to our expression:
\[
\frac{13^{12}}{13^{-10}} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22}
\]
Thus, the simplified expression is:
\[
\boxed{13^{22}}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to our expression:
\[
\frac{13^{12}}{13^{-10}} = 13^{12 - (-10)} = 13^{12 + 10} = 13^{22}
\]
Thus, the simplified expression is:
\[
\boxed{13^{22}}
\]