Question

simplify the expression ((y^{6}z^{9})(6y^{4}z^{2})). write the variables in alphabetical order.

Explanation:

Step1: Multiply the coefficients and like variables

First, multiply the coefficient (1 for the first term and 6 for the second term) and then use the product rule for exponents \(a^m \cdot a^n = a^{m + n}\) for the variables \(y\) and \(z\) separately.
For the coefficient: \(1\times6 = 6\)
For the variable \(y\): \(y^{6}\cdot y^{4}=y^{6 + 4}=y^{10}\) (using the product rule of exponents)
For the variable \(z\): \(z^{9}\cdot z^{2}=z^{9+ 2}=z^{11}\) (using the product rule of exponents)

Step2: Combine the results

Combine the coefficient and the simplified variables. The variables should be in alphabetical order, so we write \(y\) before \(z\).
So the simplified expression is \(6y^{10}z^{11}\)

Answer:

\(6y^{10}z^{11}\)