(3m%5E2n%5E4)%5E2.jpeg "(-2mn)(3m^2n^4)^2")
Simplifying the Expression (-2mn)(3m^2n^4)^2
This article will guide you through the steps of simplifying the expression (-2mn)(3m^2n^4)^2.
Understanding the Order of Operations
To simplify this expression, we'll follow the order of operations, commonly 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
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Simplify the exponent:
- (3m^2n^4)^2 = (3m^2n^4) * (3m^2n^4) = 9m^4n^8
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Multiply the terms:
- (-2mn) * (9m^4n^8) = -18m^5n^9
Final Result
Therefore, the simplified form of (-2mn)(3m^2n^4)^2 is -18m^5n^9.
Key Points
- Exponent Rule: When raising a product to a power, apply the power to each factor within the parentheses.
- Coefficient Multiplication: Multiply the coefficients outside the parentheses with the coefficient obtained after simplifying the exponent.
- Variable Multiplication: When multiplying variables with the same base, add the exponents.
By following these steps, you can effectively simplify any similar expression involving exponents and products.