9514 1404 393
Answer:
16
Step-by-step explanation:
There are several ways to go at this. Perhaps the simplest is to put the expression into your calculator.
__
Using the rules of exponents, you recognize ...
a^-b = 1/a^b
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
__
So, we can rewrite the expression to be ...
[tex]\displaystyle\frac{1}{2}\cdot\left(\frac{1}{2}\right)^{-5}=2^{-1}\cdot(2^{-1})^-5\\\\=2^{-1}\cdot2^{(-1)(-5)}=2^{-1}\cdot2^5\\\\=2^{-1+5}=2^4=\boxed{16}[/tex]
