Question

multiply.
\\(\frac{15x}{4b} \cdot \frac{2b^5x^2}{5x}\\)
simplify your answer as much as possible.

Explanation:

Step1: Multiply numerators and denominators

Multiply the numerators together: \(15x \cdot 2b^5x^2 = 30x^{1 + 2}b^5 = 30x^3b^5\)
Multiply the denominators together: \(4b \cdot 5x = 20bx\)
So we have \(\frac{30x^3b^5}{20bx}\)

Step2: Simplify the fraction

Simplify the coefficients: \(\frac{30}{20} = \frac{3}{2}\)
Simplify the \(x\) terms: \(\frac{x^3}{x} = x^{3 - 1} = x^2\)
Simplify the \(b\) terms: \(\frac{b^5}{b} = b^{5 - 1} = b^4\)

Combine these results: \(\frac{3}{2} \cdot x^2 \cdot b^4 = \frac{3x^2b^4}{2}\)

Answer:

\(\frac{3x^2b^4}{2}\)