Question

multiply using the product rule.
\\((-7x^2y^0z)(-4xyz^2)\\)
\\((-7x^2y^0z)(-4xyz^2) = \square\\)
(simplify your answer. type your answer using exponential notation. use positive exponents only.)

Explanation:

Step1: Recall the zero exponent rule

Any non - zero number raised to the power of 0 is 1. So, \(y^{0}=1\). The expression becomes \((- 7x^{2}\times1\times z)(-4xyz^{2})\) or \((-7x^{2}z)(-4xyz^{2})\).

Step2: Multiply the coefficients

Multiply the coefficients \(-7\) and \(-4\). \(-7\times(-4) = 28\).

Step3: Multiply the \(x\) terms

Using the product rule for exponents \(a^{m}\times a^{n}=a^{m + n}\), for the \(x\) terms \(x^{2}\times x=x^{2 + 1}=x^{3}\).

Step4: Multiply the \(y\) terms

For the \(y\) terms, we have \(y^{0}\times y = 1\times y=y^{1}=y\) (since \(y^{0} = 1\) and using \(a^{m}\times a^{n}=a^{m + n}\) with \(m = 0\) and \(n=1\)).

Step5: Multiply the \(z\) terms

Using the product rule for exponents, for the \(z\) terms \(z\times z^{2}=z^{1+2}=z^{3}\).

Step6: Combine all the parts

Multiply the results from Step 2, Step 3, Step 4 and Step 5 together. We get \(28\times x^{3}\times y\times z^{3}=28x^{3}yz^{3}\).

Answer:

\(28x^{3}yz^{3}\)