Answer:
Step-by-step explanation:
Take this one thing at a time...baby steps to help us keep our sanity. Math does tend to drive a person around the bend...
The first term is the tricky one. If the exponent is negative, it can be rewritten as a positive by putting whatever the exponent is on under a 1. For example:
[tex]x^{-2}=\frac{1}{x^2}[/tex]
So we'll use that to make this simpler.
[tex](-\frac{1}{2})^{-2}=\frac{1}{(-\frac{1}{2})^2 } }[/tex] Squaring that negative makes it a positive, so we can rewrite as
[tex]\frac{1}{(\frac{1}{2})^2 }[/tex] which simplifies to
[tex]\frac{1}{\frac{1}{4} }[/tex] What we have there is a fraction over a fraction; namely:
[tex]\frac{\frac{1}{1} }{\frac{1}{4} }[/tex] and the rule for that is to bring the bottom fraction up, flip it and multiply:
[tex]\frac{1}{1}[/tex] × [tex]\frac{4}{1}[/tex] which is 4.
Now for the second part. All we are doing here is squaring that fraction. Remember that squaring a negative makes it a positive, so
[tex](-\frac{1}{2})^2=\frac{1}{4}[/tex] . Now we'll put these together to get the sum
[tex]4+\frac{1}{4}[/tex] and with a common denominator of 4, this becomes
[tex]\frac{16}{4}+\frac{1}{4}[/tex] and that equals
[tex]\frac{17}{4}[/tex], the seond choice down.
