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Simplifying Expressions with Exponents: (3a²b⁴)(-8ab³)
This article will guide you through simplifying the expression **(3a²b⁴)(-8ab³) **by breaking down the process and explaining the key concepts.
Understanding the Concepts
- Exponents: Represent repeated multiplication. For example, a² means a * a.
- Multiplication of variables: When multiplying variables with exponents, we add the exponents together. For example, a² * a³ = a⁵.
- Multiplication of coefficients: Numbers multiplying variables are called coefficients. Multiply coefficients normally.
Simplifying the Expression
- Multiply the coefficients: 3 * -8 = -24
- Multiply the 'a' variables: a² * a = a³ (remember to add the exponents)
- Multiply the 'b' variables: b⁴ * b³ = b⁷ (add the exponents)
Putting it Together
Combining the results from steps 1-3, we get: -24a³b⁷
Final Answer
Therefore, the simplified form of the expression (3a²b⁴)(-8ab³) is -24a³b⁷.