(4ab%5E5)(6a%5E3b%5E2).jpeg "(-2a^2b^3)(4ab^5)(6a^3b^2)")
Simplifying Algebraic Expressions: (-2a²b³)(4ab⁵)(6a³b²)
This article will guide you through the process of simplifying the algebraic expression (-2a²b³)(4ab⁵)(6a³b²). We will break down the steps and explain the concepts involved in simplifying this expression.
Understanding the Basics
The expression consists of three terms multiplied together. Each term is a combination of variables (a and b) and coefficients.
- Coefficient: A numerical factor in a term. For example, in the term -2a²b³, -2 is the coefficient.
- Variable: A symbol representing an unknown quantity. For example, 'a' and 'b' are variables.
- Exponent: A small number written above and to the right of a variable or number that indicates how many times the base is multiplied by itself. For example, in a², the exponent is 2, meaning a is multiplied by itself twice (a * a).
Simplifying the Expression
To simplify the expression, we follow these steps:
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Multiply the coefficients: (-2) * (4) * (6) = -48
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Multiply the variables with the same base:
- For 'a': a² * a * a³ = a⁶ (When multiplying variables with the same base, add their exponents)
- For 'b': b³ * b⁵ * b² = b¹⁰
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Combine the results: -48 * a⁶ * b¹⁰ = -48a⁶b¹⁰
Therefore, the simplified form of the expression (-2a²b³)(4ab⁵)(6a³b²) is -48a⁶b¹⁰.
Key Points to Remember
- Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when dealing with algebraic expressions. This ensures consistent results.
- Combining like terms: You can only add or subtract terms with the same variables and exponents.
- Exponent Rules: Understand the rules for multiplying and dividing variables with exponents.
By applying these concepts, you can simplify complex algebraic expressions effectively.