Solving for Reciprocal: Calculating (7/8) to the Negative Power

To solve the problem of evaluating $(\frac{7}{8})^{-2}$, we'll proceed with these steps:

• Step 1: Convert the negative exponent into a positive exponent by taking the reciprocal of the base.
• Step 2: Evaluate the expression obtained after the conversion.

Now, let's work through each step:

Step 1: Convert the negative exponent to a positive exponent using the reciprocal:
Using the property $(\frac{a}{b})^{-n} = (\frac{b}{a})^{n}$, we have:

$(\frac{7}{8})^{-2} = (\frac{8}{7})^{2}$

Step 2: Calculate the positive power:

$(\frac{8}{7})^{2} = \frac{8^2}{7^2} = \frac{64}{49}$

Thus, the solution to the problem is:
$(\frac{7}{8})^{-2} = \frac{64}{49}$

Extra step to express $\frac{64}{49}$ as a mixed number:

$64 \div 49 = 1$ remainder $15$, so $\frac{64}{49} = 1 \frac{15}{49}$.

Therefore, the simplified solution to the expression $(\frac{7}{8})^{-2}$ is $1 \frac{15}{49}$.