Step-by-step explanation:
[tex]\bf a)~2\cdot2^{-3} = 2^{1-3} =2^{-2}=\dfrac{1}{2^{2}} =\blue{\dfrac{1}{4}}[/tex]
[tex]\bf b)~~\bigg(\dfrac{1}{4}\bigg)^{-2} \cdot 4= 4^{2} \cdot 4=4^{1+2}=4^{3}=\purple{64}[/tex]
[tex]\bf c)~~\dfrac{\big(3^{-2}\big)^{3}\cdot 27^{2}}{3} =\dfrac{3^{-2\cdot3}\cdot (3^{3})^{2}}{3}=[/tex]
[tex]\bf \dfrac{3^{-6}\cdot 3^{3\cdot2}}{3}=\dfrac{3^{-6}\cdot 3^{6}}{3}= \dfrac{\dfrac{1}{\not3^{6}}\cdot \not3^{6}}{3}=\red{\dfrac{1}{3}}[/tex]
[tex]==Salmon==[/tex]
