https://file.aiquickdraw.com/mathbot/file/1728924647615scmixqpj.jpg

The expression in the image is:

\[
\left( -\frac{1}{2} \right)^{-2} \times 2^2 \div \left( \frac{1}{2} \right)^{-5} + \left( \sqrt{7} \right)^0
\]

Let's break this down step by step:

1. **Evaluate \(\left( -\frac{1}{2} \right)^{-2}\)**:
   Using the rule \((a^{-n}) = \frac{1}{a^n}\), we get:
   \[
   \left( -\frac{1}{2} \right)^{-2} = \frac{1}{\left( -\frac{1}{2} \right)^2} = \frac{1}{\frac{1}{4}} = 4
   \]

2. **Evaluate \(2^2\)**:
   \[
   2^2 = 4
   \]

3. **Evaluate \(\left( \frac{1}{2} \right)^{-5}\)**:
   Again using the same rule:
   \[
   \left( \frac{1}{2} \right)^{-5} = \frac{1}{\left( \frac{1}{2} \right)^5} = \frac{1}{\frac{1}{32}} = 32
   \]

4. **Evaluate \(\left( \sqrt{7} \right)^0\)**:
   Any number raised to the power of 0 is 1:
   \[
   \left( \sqrt{7} \right)^0 = 1
   \]

Now substitute these values into the expression:

\[
4 \times 4 \div 32 + 1
\]

5. **Simplify**:

First, calculate \(4 \times 4 = 16\).

Next, divide \(16 \div 32 = \frac{1}{2}\).

Now add \(1\):

\[
\frac{1}{2} + 1 = \frac{3}{2}
\]

So, the final result is:

\[
\boxed{\frac{3}{2}}
\]

Would you like more details on any step? Here are some related questions:

1. What are the laws of exponents used in solving this?
2. How do you handle negative exponents in different scenarios?
3. Can you simplify a complex expression involving radicals and powers?
4. What is the rule for raising any number to the power of zero?
5. How do you perform division involving fractions and powers?

**Tip**: Always simplify exponents before doing multiplication or division to make calculations easier.

Simplify the expression: (-1/2)^-2 × 2^2 ÷ (1/2)^-5 + (√7)^0

Learn how to simplify the expression (-1/2)^-2 × 2^2 ÷ (1/2)^-5 + (√7)^0 with a detailed step-by-step solution. This problem covers key mathematical concepts like exponentiation, radicals, and the laws of exponents, suitable 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