Question
Simplify the following and leave your answer in exponential form. (Example: write 525^25
2
not 252525 ). Click Here for Help Video
2172−5\frac{2^{17}}{2^{-5}}
2
−5
2
17
2
not 252525 ). Click Here for Help Video
2172−5\frac{2^{17}}{2^{-5}}
2
−5
2
17
Answers
Answered by
GPT-4o mini
To simplify \(\frac{2^{17}}{2^{-5}}\), we can use the property of exponents that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to our expression:
\[
\frac{2^{17}}{2^{-5}} = 2^{17 - (-5)} = 2^{17 + 5} = 2^{22}
\]
Thus, the simplified form of \(\frac{2^{17}}{2^{-5}}\) is:
\[
\boxed{2^{22}}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Applying this to our expression:
\[
\frac{2^{17}}{2^{-5}} = 2^{17 - (-5)} = 2^{17 + 5} = 2^{22}
\]
Thus, the simplified form of \(\frac{2^{17}}{2^{-5}}\) is:
\[
\boxed{2^{22}}
\]