Question

1. simplify: (5x⁴y³)(2x²y⁻¹) / (10x³y)

a. x³y
b. x³/y
c. xy³
d. x²y²

Explanation:

Step1: Multiply the numerator terms

First, multiply the coefficients and use the rule of exponents \(a^m \cdot a^n = a^{m + n}\) for the variables.
For the coefficients: \(5\times2 = 10\)
For \(x\) terms: \(x^{4}\cdot x^{2}=x^{4 + 2}=x^{6}\)
For \(y\) terms: \(y^{3}\cdot y^{-1}=y^{3+( - 1)}=y^{2}\)
So the numerator becomes \(10x^{6}y^{2}\)

Step2: Divide by the denominator

Now divide the numerator \(10x^{6}y^{2}\) by the denominator \(10x^{3}y\).
For the coefficients: \(\frac{10}{10}=1\)
For \(x\) terms: \(\frac{x^{6}}{x^{3}}=x^{6 - 3}=x^{3}\) (using the rule \(\frac{a^m}{a^n}=a^{m - n}\))
For \(y\) terms: \(\frac{y^{2}}{y}=y^{2 - 1}=y\)

Combining these, we get \(x^{3}y\)

Answer:

A. \(x^{3}y\)