Answer:
n = - 3
Step-by-step explanation:
Using the properties of exponents
• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
• [tex]a^{-n}[/tex] ⇔ [tex]\frac{1}{a^{n} }[/tex]
given
[tex](10^4)^{n}[/tex] = [tex]\frac{1}{10^{12} }[/tex] , then
[tex]10^{4n}[/tex] = [tex]10^{-12}[/tex]
since the bases on both sides are the same, equate the exponents
4n = - 12 ( divide both sides by 4 )
n = - 3
