When [tex]$6 a^2 b^3 \cdot -3 a^5 b^3$[/tex] is multiplied, the product of the coefficients is $\square$
Answer (1)
The problem asks for the product of the coefficients in the expression 6 a 2 b 3 \tcdot − 3 a 5 b 3 .
Identify the coefficients as 6 and − 3 .
Multiply the coefficients: 6 \tcdot − 3 = − 18 .
The product of the coefficients is − 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 this expression is multiplied.
Multiplying the Coefficients The coefficients in the expression are 6 and − 3 . To find the product of the coefficients, we simply multiply these two numbers: 6 \tcdot − 3 = − 18 .
Final Answer Therefore, the product of the coefficients is − 18 .
Examples
In physics, when calculating forces or energies involving multiple objects, you often multiply coefficients that represent physical constants or quantities. For example, if you are calculating the gravitational force between two objects, you multiply the gravitational constant by the masses of the objects and divide by the square of the distance between them. The product of the coefficients gives you the overall scaling factor for the force.
