Question

multiply.
\\(\frac{6b}{2a} \cdot \frac{4ab}{3b}\\)
simplify your answer as much as possible.

Explanation:

Step1: Multiply numerators and denominators

Multiply the numerators \(6b\) and \(4ab\), and the denominators \(2a\) and \(3b\). So we get \(\frac{6b\times4ab}{2a\times3b}\).

Step2: Simplify the expression

First, calculate the product in the numerator: \(6b\times4ab = 24ab^2\). Then, calculate the product in the denominator: \(2a\times3b = 6ab\). Now we have \(\frac{24ab^2}{6ab}\).
Next, simplify the fraction by dividing the coefficients and subtracting the exponents of like variables. For the coefficients, \(\frac{24}{6}=4\). For the variable \(a\), \(\frac{a}{a}=a^{1 - 1}=a^0 = 1\) (we can ignore \(a^0\) as it is 1). For the variable \(b\), \(\frac{b^2}{b}=b^{2 - 1}=b\). So multiplying these results together, we get \(4\times1\times b = 4b\).

Answer:

\(4b\)