( m-⁴ n² o-⁵)⁶ / ( m³ n-⁶ o²)-⁴

We are given the following expression:

\[
\frac{(m^{-4} n^2 o^{-5})^6}{(m^3 n^{-6} o^2)^{-4}}
\]

Let's solve this step by step:

### Step 1: Apply the power of a power rule
When raising a power to another power, multiply the exponents:

\[
(m^{-4} n^2 o^{-5})^6 = m^{-24} n^{12} o^{-30}
\]
\[
(m^3 n^{-6} o^2)^{-4} = m^{-12} n^{24} o^{-8}
\]

Now, the expression looks like:

\[
\frac{m^{-24} n^{12} o^{-30}}{m^{-12} n^{24} o^{-8}}
\]

### Step 2: Use the quotient rule for exponents
The quotient rule states that for any base \( a \), \( \frac{a^m}{a^n} = a^{m-n} \).

Apply this to each base:

\[
m^{-24 - (-12)} = m^{-24 + 12} = m^{-12}
\]
\[
n^{12 - 24} = n^{-12}
\]
\[
o^{-30 - (-8)} = o^{-30 + 8} = o^{-22}
\]

### Final Answer:
\[
m^{-12} n^{-12} o^{-22}
\]

This can be rewritten as:

\[
\frac{1}{m^{12} n^{12} o^{22}}
\]

---

Would you like more details on any of the steps? Here are five questions to deepen understanding:

1. How does the power of a power rule work?
2. Can the quotient rule for exponents apply to negative exponents?
3. Why do we add exponents when dividing like bases?
4. How do negative exponents affect the final expression?
5. What happens if any base had a zero exponent?

**Tip:** Always simplify powers before combining terms to avoid mistakes.

(m⁻⁴ n² o⁻⁵)⁶ / (m³ n⁻⁶ o²)⁻⁴

Learn how to simplify the expression (m⁻⁴ n² o⁻⁵)⁶ / (m³ n⁻⁶ o²)⁻⁴ using the laws of exponents. This detailed step-by-step solution applies the power of a power rule and the quotient rule for exponents. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation