Let's break down the expression step by step:

Given:
\[
5^2 \times \left(\frac{1}{125}\right)^{-1} \div 25
\]

### Step 1: Simplify \( 5^2 \)
\[
5^2 = 25
\]

### Step 2: Simplify \( \left(\frac{1}{125}\right)^{-1} \)
Taking the reciprocal of \( \frac{1}{125} \) gives:
\[
\left(\frac{1}{125}\right)^{-1} = 125
\]

### Step 3: Multiply the results from Step 1 and Step 2
\[
25 \times 125 = 3125
\]

### Step 4: Divide by 25
\[
\frac{3125}{25} = 125
\]

Thus, the value of the expression is:
\[
\boxed{125}
\]

Do you want more details, or have any questions?

Here are 5 related questions:
1. How do you calculate powers of numbers?
2. What are the rules for dealing with negative exponents?
3. How do you simplify expressions with both multiplication and division?
4. What is the relationship between exponents and roots?
5. How can you apply exponent rules to more complex expressions?

**Tip**: Remember that any number raised to a negative exponent flips the fraction (reciprocal).

This detailed step-by-step solution walks through the process of simplifying the exponential expression 5^2 * (1/125)^-1 / 25. The solution covers key math concepts like exponents, negative exponents, reciprocals, and multiplication. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation