Question

multiply.
\frac{2x^{3}}{3bx} \cdot \frac{15b}{8x}
simplify your answer as much as possible.

Explanation:

Step1: Multiply numerators and denominators

Multiply the numerators \(2x^{3}\) and \(15b\), and the denominators \(3bx\) and \(8x\). So we get \(\frac{2x^{3}\times15b}{3bx\times8x}\).

Step2: Simplify the coefficients and variables

First, simplify the coefficients: \(2\times15 = 30\) and \(3\times8 = 24\). Then for the variables, \(x^{3}\times x = x^{4}\) in the numerator? Wait, no, wait. Wait, numerator: \(2x^{3}\times15b = 30x^{3}b\). Denominator: \(3bx\times8x = 24bx^{2}\). Now, cancel out common factors. The \(b\) in numerator and denominator cancels. Then \(x^{3}/x^{2}=x\), and \(30/24\) simplifies to \(5/4\) (divide numerator and denominator by 6: \(30\div6 = 5\), \(24\div6 = 4\)). So putting it together: \(\frac{5x}{4}\). Wait, let's check again. Wait, numerator: \(2x^{3} \times 15b = 30x^{3}b\). Denominator: \(3bx \times 8x = 24bx^{2}\). Now, cancel \(b\) from numerator and denominator: \(30x^{3}/24x^{2}\). Then \(30/24 = 5/4\), and \(x^{3}/x^{2}=x\). So yes, \(\frac{5x}{4}\).

Answer:

\(\frac{5x}{4}\)