Answer
$16zn^3 \left( zn^{3}+4n^{4}-2z^{2} \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Get the $GCF$ of each term of the given expression, $
16z^2n^6+64zn^7-32z^3n^3
.$ Divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient.
$\bf{\text{Solution Details:}}$
Using the $GCF=
16zn^3
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
16zn^3 \left( \dfrac{16z^2n^6}{16zn^3}+\dfrac{64zn^7}{16zn^3}-\dfrac{32z^3n^3}{16zn^3}
\right)
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
16zn^3 \left( z^{2-1}n^{6-3}+4z^{1-1}n^{7-3}-2z^{3-1}n^{3-3} \right)
\\\\=
16zn^3 \left( z^{1}n^{3}+4z^{0}n^{4}-2z^{2}n^{0} \right)
\\\\=
16zn^3 \left( zn^{3}+4(1)n^{4}-2z^{2}(1) \right)
\\\\=
16zn^3 \left( zn^{3}+4n^{4}-2z^{2} \right)
.\end{array}
