Question

1. (5n·9)·2n

Explanation:

Step1: Use associative property of multiplication

We can rearrange the factors using the associative property of multiplication, which states that \((a \cdot b) \cdot c = a \cdot (b \cdot c)\). So, \((5n \cdot 9) \cdot 2n = 5n \cdot 9 \cdot 2n\). Then, we can group the coefficients and the variables separately: \((5 \cdot 9 \cdot 2) \cdot (n \cdot n)\).

Step2: Multiply the coefficients and the variables

First, multiply the coefficients: \(5 \cdot 9 \cdot 2 = 90\). Then, multiply the variables using the rule of exponents \(a^m \cdot a^n = a^{m + n}\). Here, \(n \cdot n = n^{1 + 1}=n^2\).

Step3: Combine the results

Multiply the result of the coefficients and the result of the variables: \(90 \cdot n^2 = 90n^2\).

Answer:

\(90n^2\)