Questions: Simplify. 40 x y z / 4 y z

Solution Steps

To simplify the given ratio of multivariate monomials, we need to divide the coefficients and then apply the properties of exponents to the variables. Specifically, we will divide the coefficients (40 by 4) and cancel out the common variables in the numerator and the denominator.

To simplify the expression \(\frac{40xy z}{4yz}\), we start by dividing the coefficients. The coefficient in the numerator is 40, and the coefficient in the denominator is 4. Dividing these gives:

\[ \frac{40}{4} = 10 \]

Next, we simplify the variables. The expression in the numerator is \(xy z\) and in the denominator is \(yz\). We can cancel out the common variables \(y\) and \(z\) from both the numerator and the denominator:

\[ \frac{xy z}{yz} = x \]

Combining the results from the previous steps, the simplified expression is:

\[ 10 \times x = 10x \]

Final Answer