Answer:
1. [tex]\frac{(-5k^{2}m)(2km)^{4} (3km^{4}) ^{2}}{k^{2}m^{3}}[/tex] = -720[tex]k^{6}m^{10}[/tex]
2. [tex]\frac{3m}{m^{4} }[/tex] = [tex]\frac{3}{m^{3} }[/tex] (or 3[tex]m^{-3}[/tex])
Step-by-step explanation:
1. The given expression is:
[tex]\frac{(-5k^{2}m)(2km)^{4} (3km^{4}) ^{2}}{k^{2}m^{3}}[/tex]
With respect to the principle of exponential, we have;
[tex]\frac{(-5k^{2}m)(2^{4}k^{4} m^{4})(3^{2}k^{2}m^{8})}{k^{2} m^{3} }[/tex] = [tex]\frac{(-5k^{2}m)(16k^{4} m^{4})(9k^{2}m^{8} }{k^{2}m^{3} }[/tex]
Applying the law of indices,
= [tex]\frac{(-5*16*9)(k^{2+4+2})(m^{1+4+8}) }{k^{2} m^{3} }[/tex]
= [tex]\frac{-720k^{8} m^{13} }{k^{2}m^{3} }[/tex]
= -720[tex]k^{8}m^{13}[/tex] x [tex]k^{-2} m^{-3}[/tex]
= -720[tex]k^{8-2} m^{13-3}[/tex]
= -720[tex]k^{6}m^{10}[/tex]
2. [tex]\frac{3m}{m^{4} }[/tex]
divide the numerator and denominator with common factor m,
= [tex]\frac{3}{m^{3} }[/tex]
This can not be simplified further since there are no more common factors, so that;
[tex]\frac{3m}{m^{4} }[/tex] = [tex]\frac{3}{m^{3} }[/tex] (or 3[tex]m^{-3}[/tex])
