Question

please solve this problems

Answer 1

[tex]1 ) 512^{ \frac{-2}{9} } = (2^{9})^( \frac{-2}{9})= 2^{-2} = \frac{1}{4} \\ 2) (216^{ \frac{2}{3} })^ \frac{1}{2} = ((6^{3})^ \frac{2}{3})^ \frac{1}{2}=36^{ \frac{1}{2} }=6 \\ 3) 8^{ \frac{-1}{3} }= (2^{3})^ \frac{-1}{3} = \frac{1}{2} \\ Now, \frac{10}{1/2} = 20 \\ 4) 16^{ \frac{3}{4} } = (2^{4})^ \frac{3}{4} = 2^{3}=8 \\ 5) 27^{ \frac{1}{3} } = (3^{3})^ \frac{1}{3}=3 \\ 16^{ \frac{-1}{4} }=(2^4)^( \frac{-1}{4})= 2^{-1} =1/2 \\ 27^{ \frac{1}{3} } * 16^{ \frac{-1}{4} }=3/2 \\ [/tex]
[tex]6) ((3^{4})^( \frac{1}{2}))^-2= (3^{2})^(-2)= 3^{-4}=x \\ Now, \frac{1}{x} = \frac{1}{ 3^{-4} } = 3^{4} =81[/tex]