When [tex]$6 a^2 b^3 \cdot -3 a^5 b^3$[/tex] is multiplied, the product of the coefficients is $\square$
Answer (2)
Identify the coefficients: 6 and -3.
Multiply the coefficients: 6 \tcdot − 3 .
Perform the multiplication: 6 \tcdot − 3 = − 18 .
State the final answer: − 18 .
Explanation
Understanding the Problem We are given the expression 6 a 2 b 3 \tcdot − 3 a 5 b 3 . We need to find the product of the coefficients when the expression is multiplied.
Identifying the Coefficients The coefficients in the expression are 6 and -3.
Multiplying the Coefficients To find the product of the coefficients, we multiply them together: 6 \tcdot − 3 = − 18 .
Stating the Result The product of the coefficients is -18.
Examples
In physics, when calculating forces or energies involving multiple components, you often multiply coefficients to determine the overall magnitude. For instance, if you have two forces acting on an object, where one force is 6 a 2 b 3 and the other is − 3 a 5 b 3 , the product of their coefficients (-18) helps determine the combined effect on the object's motion or energy. This concept is crucial for understanding how different factors combine to influence physical phenomena.
The product of the coefficients when multiplying 6 a 2 b 3 and − 3 a 5 b 3 is − 18 .
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