The expression [tex]\frac{9^{-3}}{9^{12} }[/tex] written in the form [tex]9^{n}[/tex] is [tex]9^{-15}[/tex]
From the question,
we are to rewrite the given expression (9^-3/9^12) in the form 9^n
First, write the expressions properly.
The given expression is
[tex]\frac{9^{-3}}{9^{12} }[/tex]
To rewrite the given expression in the form [tex]9^{n}[/tex], we will use the division law of indices
From the division law of indices, we have that
[tex]x^{y} \div x^{z}= x^{y-z}[/tex]
Then, the given expression becomes
[tex]\frac{9^{-3}}{9^{12} } = 9^{-3} \div 9^{12}[/tex]
[tex]= 9^{-3-12}[/tex]
[tex]=9^{-15}[/tex]
Hence, the expression [tex]\frac{9^{-3}}{9^{12} }[/tex] written in the form [tex]9^{n}[/tex] is [tex]9^{-15}[/tex]
Learn more here: https://brainly.com/question/18205419
