Simplify the following: $\left(-3 p^4\right)\left(2 p^3\right)\left(p^2\right) =
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Answer (1)
Multiply the coefficients: − 3 × 2 × 1 = − 6 .
Multiply the variable terms by adding the exponents: p 4 × p 3 × p 2 = p 4 + 3 + 2 = p 9 .
Combine the results to obtain the simplified expression: − 6 p 9 .
The simplified expression is − 6 p 9 .
Explanation
Understanding the Problem We are given the expression ( − 3 p 4 ) ( 2 p 3 ) ( p 2 ) and we need to simplify it.
Plan of Action To simplify the expression, we will first multiply the coefficients and then multiply the variable terms using the exponent rules.
Multiplying Coefficients First, let's multiply the coefficients: − 3 × 2 × 1 = − 6 .
Multiplying Variables Next, let's multiply the variable terms. Recall that when multiplying terms with the same base, we add the exponents: p 4 × p 3 × p 2 = p 4 + 3 + 2 = p 9 .
Combining Results Now, combine the results from the previous steps to get the simplified expression: − 6 p 9 .
Final Answer Therefore, the simplified expression is − 6 p 9 .
Examples
Simplifying expressions like this is fundamental in algebra and is used in various fields such as physics and engineering. For example, when calculating the volume of a complex shape or determining the energy of a system, you might need to simplify polynomial expressions. Imagine you are designing a rectangular prism where the length is − 3 p 4 , the width is 2 p 3 , and the height is p 2 . The volume of the prism would be the product of these dimensions, which simplifies to − 6 p 9 .
