https://file.aiquickdraw.com/mathbot/file/17322589169413vahlgno.jpg

Let’s simplify the given expression step by step.

The problem is to simplify:

\[
\frac{(a^3b^4c^2)^2}{ab^4c^3}
\]

### Step 1: Expand the numerator
Using the power rule \((x^m)^n = x^{m \cdot n}\), expand \((a^3b^4c^2)^2\):

\[
(a^3b^4c^2)^2 = a^{3 \cdot 2}b^{4 \cdot 2}c^{2 \cdot 2} = a^6b^8c^4
\]

So the numerator becomes \(a^6b^8c^4\).

### Step 2: Simplify the division
Divide the expanded numerator by the denominator \(ab^4c^3\):

\[
\frac{a^6b^8c^4}{ab^4c^3}
\]

Using the division rule \(x^m / x^n = x^{m-n}\), simplify each variable:

1. For \(a\): \(a^6 / a = a^{6-1} = a^5\)
2. For \(b\): \(b^8 / b^4 = b^{8-4} = b^4\)
3. For \(c\): \(c^4 / c^3 = c^{4-3} = c^1 = c\)

### Final Answer:
The simplified expression is:

\[
a^5b^4c
\]

The correct option is:

**A. \(a^5b^4c\)**

---

Would you like further details or assistance with related concepts? Here are some questions for deeper exploration:

1. What are the general rules of exponents used in simplification?
2. How does the power rule apply to multiple variables in a term?
3. What is the difference between simplifying powers and multiplying powers?
4. Can you explain why \(c^{4-3} = c^1\) and not just \(c\)?
5. How do we handle cases where the exponent becomes negative in division?

**Tip:** Always apply exponent rules systematically to avoid missing terms.

The simplest form of \(\frac{(a^3b^4c^2)^2}{ab^4c^3}\) is…

Step-by-step solution for simplifying the expression (a^3b^4c^2)^2 / ab^4c^3. This problem involves applying exponent rules to simplify powers and perform division. Perfect for students in Grades 8-10 learning about exponent laws.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation