Answer:
Step-by-step explanation:
[tex]1000^{m}[/tex] ÷ [tex]100^{n}[/tex] = [tex]\dfrac{(10^{3})^{m}}{(10^{2})^{n}}[/tex]
[tex]= \dfrac{10^{3m}}{10^{2n}}[/tex] [tex]{(x^{a})^{b}=a^{a*b}}[/tex]
[tex]= 10^{3m-2n} = 10^{z}[/tex]
z = 3m-2n
[tex]1000^{m}[/tex] ÷ [tex]100^{n}[/tex]
= [tex]10^{3m}[/tex] ÷ [tex]10^{2n}[/tex]
= [tex]10^{3m - 2n}[/tex] = [tex]10^{z}[/tex]
=> z = 3m - 2n
