Simplify the following: $\left(-3 p^4\right)\left(2 p^3\right)\left(p^2\right) = $
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 asked to simplify the expression \left(-3 p^4\right)\\left(2 p^3\right)\\left(p^2\right) . This involves multiplying terms with coefficients and variables raised to powers.
Multiplying Coefficients First, we multiply the coefficients: − 3 × 2 × 1 = − 6 .
Multiplying Variables Next, we multiply the variable terms. When multiplying variables with exponents, we add the exponents: p 4 × p 3 × p 2 = p 4 + 3 + 2 = p 9 .
Combining Results Finally, we combine the coefficient and the variable term to get the simplified expression: − 6 p 9 .
Final Answer Therefore, the simplified expression is − 6 p 9 .
Examples
Understanding how to simplify expressions with exponents is crucial in many areas, such as calculating the area or volume of geometric shapes. For example, if you have a rectangular prism with sides defined by polynomial expressions, simplifying the expression for its volume (length \times width \times height) involves similar steps of multiplying coefficients and adding exponents. This skill is also fundamental in physics for calculations involving motion and energy, where variables are often raised to powers.
