ANSWER
-31/2
EXPLANATION
We have to sum these two numbers and write the answer as a fraction.
Note that the second term has a negative exponent, which by the negative exponents rule we can rewrite as a fraction where the denominator is the base raised to the same exponent but positive,
[tex]2^{-1}=\frac{1}{2}[/tex]
Replacing into the expression,
[tex]-2^4+2^{-1}=-2^4+\frac{1}{2}[/tex]
To add, the common denominator is 2. Then we multiply it by the first term,
[tex]-2^4+\frac{1}{2}=\frac{-2\cdot2^4+1}{2}[/tex]
Solve the power and multiply,
[tex]\frac{-2\cdot16+1}{2}=\frac{-32+1}{2}[/tex]
And add,
[tex]\frac{-32+1}{2}=\frac{-31}{2}[/tex]
Hence, the answer is -31/2.
