(4a%5E5b%5E3)%5E3.jpeg "(-3a^2b^2)(4a^5b^3)^3")
Simplifying the Expression (-3a^2b^2)(4a^5b^3)^3
This article will guide you through simplifying the expression (-3a^2b^2)(4a^5b^3)^3.
Understanding the Order of Operations
Before we begin simplifying, let's recall the order of operations, often remembered by the acronym PEMDAS or BODMAS:
- Parentheses / Brackets
- Exponents / Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Simplifying the Expression
-
Simplify the exponent: We start by simplifying the term within the parentheses raised to the power of 3.
(4a^5b^3)^3 = 4^3 * (a^5)^3 * (b^3)^3 = 64a^15b^9
-
Multiply the terms: Now, we multiply the simplified term with the term outside the parentheses.
(-3a^2b^2)(64a^15b^9) = -3 * 64 * a^2 * a^15 * b^2 * b^9 = -192a^17b^11
Final Result
Therefore, the simplified form of the expression (-3a^2b^2)(4a^5b^3)^3 is -192a^17b^11.