Math Problem Statement

If m = 4 and n = 3, find the value of the expression (5^m * 5^2) / 5^n

Solution

The expression to solve is:

5m525n\frac{5^m \cdot 5^2}{5^n} where m=4m = 4 and n=3n = 3.

Step 1: Substitute the values of mm and nn into the expression:

545253\frac{5^4 \cdot 5^2}{5^3}

Step 2: Apply the laws of exponents.

Recall that for multiplication, we add exponents: 5452=54+2=565^4 \cdot 5^2 = 5^{4+2} = 5^6 So the expression becomes: 5653\frac{5^6}{5^3}

Step 3: Simplify the division of exponents.

For division, we subtract exponents: 5653=563=53\frac{5^6}{5^3} = 5^{6-3} = 5^3

Thus, the final result is: 53=1255^3 = 125

The answer is 125125.

Would you like more details or have any questions?


Here are 5 related questions you could explore:

  1. What happens if m=5m = 5 and n=2n = 2?
  2. How does the division of powers work for other bases, like 7 or 10?
  3. Can you explain the laws of exponents in more detail?
  4. How would the result change if the exponents were negative?
  5. What if the entire expression was raised to another exponent?

Tip: When working with powers, always remember to simplify using the exponent rules: add for multiplication and subtract for division.

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Math Problem Analysis

Mathematical Concepts

Exponents
Exponent Laws
Simplifying Expressions

Formulas

Multiplication of Powers: a^m * a^n = a^(m+n)
Division of Powers: a^m / a^n = a^(m-n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10