Multiply the monomials.
$\left(\frac{2}{7} n m^2\right)\left(28 n m^3\right)=\square$
Answer (1)
Multiply the coefficients: 7 2 × 28 = 8 .
Multiply the n terms: n × n = n 2 .
Multiply the m terms: m 2 × m 3 = m 5 .
Combine the results: 8 n 2 m 5 . The final answer is 8 n 2 m 5 .
Explanation
Understanding the Problem We are asked to multiply two monomials: ( 7 2 n m 2 ) and ( 28 n m 3 ) . To do this, we will multiply the coefficients, the n terms, and the m terms separately, and then combine the results.
Multiplying Coefficients First, let's multiply the coefficients: 7 2 × 28 = 7 2 × 28 = 7 56 = 8
Multiplying n terms Next, let's multiply the n terms: n × n = n 2
Multiplying m terms Now, let's multiply the m terms: m 2 × m 3 = m 2 + 3 = m 5
Combining the Results Finally, let's combine all the results: 8 × n 2 × m 5 = 8 n 2 m 5 So, the product of the two monomials is 8 n 2 m 5 .
Examples
Monomial multiplication is used in various fields, such as physics and engineering, to calculate areas, volumes, and other quantities. For example, if you want to find the volume of a rectangular prism with sides 7 2 n , m 2 , and 28 n m 3 , you would multiply these monomials together to get the volume V = ( 7 2 n ) ( m 2 ) ( 28 n m 3 ) = 8 n 2 m 5 . This concept is also fundamental in understanding polynomial expressions and algebraic manipulations.
