Evaluate the Fraction: Finding 1/(-2)^7 Step by Step

$\frac{1}{(-2)^7}=?$

To begin with we deal with the expression in the denominator of the fraction. Making note of the power rule for exponents (raising an exponent to another exponent):

$(a^m)^n=a^{m\cdot n}$We obtain the following:

$(-2)^7=(-1\cdot2)^7=(-1)^7\cdot2^7=-1\cdot2^7=-2^7$

We then return to the initial problem and apply the above information:

$\frac{1}{(-2)^7}=\frac{1}{-2^7}=\frac{1}{-1}\cdot\frac{1}{2^7}=-\frac{1}{2^7}$$$

In the last step we remember that:

$\frac{1}{-1}=-1$

Next, we remember the Negative Exponent rule ( raising exponents to a negative power)

$a^{-n}=\frac{1}{a^n}$We apply it to the expression we obtained in the last step:

$-\frac{1}{2^7}=-2^{-7}$Let's summarize the steps of the solution:

$\frac{1}{(-2)^7}=-\frac{1}{2^7} = -2^{-7}$

$$$$Therefore, the correct answer is option C.