We have
[tex]a^b\cdot a^c=a^{b+c}[/tex]
[tex]a^b\div a^c=a^{b-c}[/tex]
So, in your case, we have
[tex]4^{-\frac{11}{3}}\div 4^{-\frac{2}{3}} = 4^{-\frac{11}{3}+\frac{2}{3}} = 4^{-\frac{9}{3}}=4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}[/tex]
Answer:
Option D. 1/64
Step-by-step explanation:
We have to simplify the following expression
[tex]4^{-\frac{11}{3} }[/tex] ÷ [tex]4^{-\frac{2}{3} }[/tex]
= [tex]\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }[/tex]
= [tex][4^{-\frac{11}{3}}[/tex] × [tex]4^{\frac{2}{3}}][/tex] [since [tex]\frac{1}{A-1}[/tex]=a]
= [tex]4^{(-\frac{11}{3}+\frac{2}{3})}[/tex] [since [tex]a^{b}[/tex] × [tex]a^{c}[/tex] = [tex]a^{(b+c)}[/tex]]
= [tex]4^{-\frac{9}{3}}[/tex]
= [tex]4^{-3}[/tex]
= [tex]\frac{1}{4^{3} }[/tex] [[tex]a^{-1}=\frac{1}{a}[/tex]]
= [tex]\frac{1}{64}[/tex]
Option D. 1/64 is the answer.
