Math Problem Statement

(7m^(-3)n^(8))^(-2) Simplify

Solution

Let's simplify the expression (7m3n8)2(7m^{-3}n^{8})^{-2} step by step.

Step 1: Apply the Power Rule to Each Factor

The expression is (7m3n8)2(7m^{-3}n^{8})^{-2}. Using the power rule (am)n=amn(a^m)^n = a^{mn}, distribute the exponent 2-2 to each factor inside the parentheses:

72(m3)2(n8)27^{-2} \cdot (m^{-3})^{-2} \cdot (n^{8})^{-2}

Step 2: Simplify Each Factor

  • For 727^{-2}: 72=172=1497^{-2} = \frac{1}{7^2} = \frac{1}{49}
  • For (m3)2(m^{-3})^{-2}: (m3)2=m6(m^{-3})^{-2} = m^{6}
  • For (n8)2(n^{8})^{-2}: (n8)2=n16(n^{8})^{-2} = n^{-16}

Step 3: Combine the Results

Now, multiply these simplified results together:

149m6n16\frac{1}{49} \cdot m^{6} \cdot n^{-16}

This simplifies to:

m649n16\frac{m^6}{49n^{16}}

So, the fully simplified expression is:

m649n16\frac{m^6}{49n^{16}}

Would you like more details or have any questions?


Here are 5 related questions:

  1. How would the expression change if the exponent was 3-3 instead of 2-2?
  2. What happens if the base includes a negative number?
  3. How do you simplify expressions with fractional exponents?
  4. What is the significance of a negative exponent in real-world contexts?
  5. How do you simplify an expression with multiple variables and exponents?

Tip: When simplifying expressions with exponents, always apply the power rule carefully to avoid mistakes.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponents
Power Rule
Simplifying Expressions

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12