To solve \(\left(\frac{7}{8}\right)^{-2}\):

1. Apply the rule of negative exponents: \( a^{-n} = \frac{1}{a^n} \). This flips the fraction:
   \[
   \left(\frac{7}{8}\right)^{-2} = \left(\frac{8}{7}\right)^2
   \]

2. Now, square the fraction:
   \[
   \left(\frac{8}{7}\right)^2 = \frac{8^2}{7^2} = \frac{64}{49}
   \]

So, \(\left(\frac{7}{8}\right)^{-2} = \frac{64}{49}\).

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:
1. What is \( \left(\frac{3}{5}\right)^{-3} \)?
2. How do you simplify \( \left(\frac{2}{9}\right)^2 \)?
3. What is the general rule for dealing with negative exponents?
4. How does one simplify \( \left(\frac{5}{7}\right)^{-1} \)?
5. What is \( \left(\frac{6}{11}\right)^{-2} \)?

**Tip:** When you see a negative exponent, remember it indicates the reciprocal of the base raised to the positive exponent.

Understand how to solve (7/8)^(-2) by applying the rule of negative exponents and fraction operations. This step-by-step solution covers key concepts like reciprocals and exponentiation. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation