Answer:
B) [tex]\frac{1}{x^{21} y^{12} }[/tex]
Step-by-step explanation:
The given expression is [tex](\frac{(x^{-3} (y^{2}) }{x^4 y^6} )^3[/tex]
Now we can bring the power 3 inside the bracket using the rule [tex](a^{m} )^n = a^{mn}[/tex]
= [tex]\frac{x^{-9}(y^6) }{x^{12}y^{18} }[/tex]
Now we have to use the quotient rule and simplify it.
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
Using the above rule, we get
= [tex]x^{-9 -12} *y^{6-18}[/tex]
= [tex]x^{-21} *y^{-12}[/tex]
Since we have a negative exponent. We can rewrite using the rule a^-m = 1/a^m
= [tex]\frac{1}{x^{21} y^{12} }[/tex]
Therefore the answer is B) [tex]\frac{1}{x^{21} y^{12} }[/tex]
