Perform the multiplication: $-0.6 a^2 b \cdot\left(-10 a b^2\right)$
Answer (1)
Multiply the coefficients: − 0.6 c d o t − 10 = 6 .
Multiply the variables with the same base by adding their exponents: a 2 c d o t a = a 2 + 1 = a 3 and b c d o t b 2 = b 1 + 2 = b 3 .
Combine the results to get the final simplified expression.
The final answer is 6 a 3 b 3 .
Explanation
Understanding the problem We are given the expression − 0.6 a 2 b ⋅ ( − 10 a b 2 ) . Our goal is to perform the multiplication and simplify the expression.
Multiplying the coefficients First, we multiply the coefficients: − 0.6 ⋅ − 10 = 6 .
Multiplying the variables Next, we multiply the variables with the same base by adding their exponents. For a , we have a 2 ⋅ a = a 2 + 1 = a 3 . For b , we have b ⋅ b 2 = b 1 + 2 = b 3 .
Combining the results Finally, we combine the results to get the simplified expression: 6 a 3 b 3 .
Examples
Understanding how to multiply algebraic expressions is fundamental in various fields, such as physics and engineering. For instance, when calculating the volume of a rectangular prism with sides defined by algebraic expressions, you need to multiply these expressions. Suppose the sides of the prism are 2 a , 3 b , and c . The volume V would be V = 2 a ⋅ 3 b ⋅ c = 6 ab c . This concept is also crucial in computer graphics for scaling and transforming objects.
