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# Simplify (ab^2 c^3) * (a^4 b^5 c^-6) / (a^-7 b^-8 c^9) * (a^10 b^11 c^-12) * (a^13 b^-14 c^15)

Efficiently simplify the expression using our guide and optimize your mathematical power.

by Maivizhi A

**Updated **Feb 26, 2024

## Simplify (ab^2 c^3) * (a^4 b^5 c^-6) / (a^-7 b^-8 c^9) * (a^10 b^11 c^-12) * (a^13 b^-14 c^15)

** While simplifying (ab^2 c^3) * (a^4 b^5 c^-6) / (a^-7 b^-8 c^9) * (a^10 b^11 c^-12) * (a^13 b^-14 c^15) is a^-11b^18c^-15**

**Explanation**

Here's a summary of the reasoning:

- Combining exponents: We combined exponents within each parenthesis and across multiplied terms, resulting in a simplified expression with terms like a^5b^7c^-3and a^16b^-11c^12.
- Canceling common terms: We identified and canceled common terms appearing in both the numerator and denominator, reducing the expression further.
- Simplifying exponents again: We combined remaining exponents where possible, like b^15b^11 to b^26, and then simplified further by canceling c^15 and c^12.
- Final result: This process led to the final simplified expression a^-11b^18c^-15.

Therefore, based on the provided steps and considering the initial expression, a^-11b^18c^-15** is the correct and complete answer. **

## Algebraic Expression and Simplification

**Here's a comprehensive explanation of algebraic expressions and simplification:**

**Algebraic Expressions:**

**Definition:**A combination of variables, numbers, and operations (like addition, subtraction, multiplication, division, and exponentiation) that represents a mathematical relationship.**Examples:**- 3x + 5y - 2
- 2a^ - 4ab + b^3
- (x + y) / (2z)
- √(x^2 + y^2)

**Simplification of Algebraic Expressions:**

Goal: To write the expression in a more concise and manageable form without changing its value.

Key Steps:

- Combine Like Terms:
- Identify terms that have the same variables and exponents.
- Add or subtract their coefficients (numerical factors).
- Example: 5x^2 + 3x^2 - 4x^2 = 4x^2

- Apply the Distributive Property:
- Multiply any factors outside of parentheses with those inside.
- Example: 2(x + 3) = 2x + 6

- Remove Parentheses:
- If no multiplication is involved, simply remove them.
- Example: (a + b) - c = a + b - c

- Simplify Exponents:
- Use rules of exponents to combine terms with the same base.
- Example: a^3 * ^2^2 = a^5

## Simplify (ab^2 c^3) * (a^4 b^5 c^-6) / (a^-7 b^-8 c^9) * (a^10 b^11 c^-12) * (a^13 b^-14 c^15) - FAQs

1. What is an algebraic expression?

An algebraic expression is a combination of variables, numbers, and operations representing a mathematical relationship.

2. Can you provide examples of algebraic expressions?

Sure! Examples include: 3x + 5y - 2, 2a^2 - 4ab + b^3, (x + y) / (2z), and √(x^2 + y^2).

3. What's the goal of simplifying algebraic expressions?

The goal is to write expressions in a more concise and manageable form without changing their value.

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