Question

1. \frac{3vu^{2}}{3vu^{0} \cdot 3u}

Explanation:

Step1: Simplify coefficients and constants

The coefficient of the numerator is 3, and the coefficient of the denominator is \(3\times0.3 = 0.9\)? Wait, no, let's re - examine the expression. The expression is \(\frac{3vu^{2}}{3vu^{0}\cdot3u}\). First, handle the coefficients: the coefficient of the numerator is 3, and the coefficient of the denominator is \(3\times3=9\)? Wait, no, the denominator is \(3vu^{0}\times3u\). Let's apply the rules of exponents and division of monomials.

For the coefficients: \(\frac{3}{3\times3}=\frac{3}{9}=\frac{1}{3}\)

For the variable \(v\): \(\frac{v}{v} = 1\) (since when dividing like bases, we subtract exponents, \(v^{1}\div v^{1}=v^{1 - 1}=v^{0}=1\))

For the variable \(u\): We have \(u^{2}\) in the numerator, \(u^{0}\) and \(u^{1}\) in the denominator. Using the rule \(a^{m}\div(a^{n}\times a^{p})=a^{m-(n + p)}\), so \(u^{2}\div(u^{0}\times u^{1})=u^{2-(0 + 1)}=u^{1}=u\)

Step2: Combine the results

Multiply the results of the coefficient, \(v\) - term, and \(u\) - term together. \(\frac{1}{3}\times1\times u=\frac{u}{3}\)

Answer:

\(\frac{u}{3}\)