Write the monomial in standard form: [tex]$0.15 p q \cdot 4 p q^2$[/tex]
Answer (2)
Multiply the coefficients: 0.15"."4 = 0.6 .
Multiply the p terms: p "." p = p 2 .
Multiply the q terms: q "." q 2 = q 3 .
Combine the results to get the monomial in standard form: 0.6 p 2 q 3 .
Explanation
Understanding the Problem We are given the monomial expression 0.15 pq "."4 p q 2 and asked to write it in standard form. This means we need to multiply the coefficients and combine like terms for the variables.
Multiplying Coefficients First, let's multiply the coefficients: 0.15 × 4 = 0.6 .
Multiplying 'p' Terms Next, let's multiply the 'p' terms: p × p = p 2 .
Multiplying 'q' Terms Now, let's multiply the 'q' terms: q × q 2 = q 1 + 2 = q 3 .
Combining the Results Finally, we combine all the results to write the monomial in standard form: 0.6 p 2 q 3 .
Examples
Understanding monomials and their standard form is crucial in various fields. For instance, when calculating the area of a rectangle with sides 0.15 p and 4 p q 2 , the area would be represented by the monomial 0.6 p 2 q 2 . Similarly, in physics, monomials can represent relationships between different physical quantities, such as force, mass, and acceleration. Mastering the manipulation of monomials lays a solid foundation for more complex algebraic concepts and real-world applications.
To write the monomial in standard form, multiply the coefficients and combine like variables. The result is 0.6 p 2 q 3 . This process shows how to simplify the expression into a single, clear form.
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