Evaluate the expression 6x^2y^-3 for x=4 and y=-2

Answer:[tex]\boxed{\bold{-12}}[/tex]Step-By-Step Explanation:Rewrite Equation[tex]\bold{\left(6\cdot \:4^2\right)\left(-2^{-3}\right)}[/tex]Remove Parenthesis: (a) = a[tex]\bold{-6\cdot \:4^2\cdot \:2^{-3}}[/tex]Factor Integer: [tex]\bold{6=2\cdot \:3}[/tex][tex]\bold{-2\cdot \:3\cdot \:4^2\cdot \:2^{-3}}[/tex]Factor Integer: [tex]\bold{4=2^2}[/tex][tex]\bold{-2\cdot \:3\left(2^2\right)^2\cdot \:2^{-3}}[/tex]Apply Exponent Rule [tex]\bold{\left(a^b\right)^c=a^{bc}: \ \left(2^2\right)^2=2^{2\cdot \:2}}[/tex][tex]\bold{-2\cdot \:3\cdot \:2^{2\cdot \:2}\cdot \:2^{-3}}[/tex]Refine[tex]\bold{-2\cdot \:3\cdot \:2^4\cdot \:2^{-3}}[/tex]Apply Exponent Rule [tex]\bold{\:a^b\cdot \:a^c=a^{b+c}: \ 2^{-3}\cdot \:2^4\cdot \:2=\:2^{1+4-3}=\:2^2}[/tex][tex]\bold{-2^2\cdot \:3}[/tex]Simplify [tex]\bold{2^2=4}[/tex][tex]\bold{-3\cdot \:4}[/tex]Multiply: [tex]\bold{3\cdot \:4=12}[/tex]Apply Negative Sign[tex]\bold{-12}[/tex]