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]
