1.
= -720![k^{6}m^{10}](/tpl/images/1060/3536/67b84.png)
2.
=
(or 3
)
Step-by-step explanation:
1. The given expression is:
![\frac{(-5k^{2}m)(2km)^{4} (3km^{4}) ^{2}}{k^{2}m^{3}}](/tpl/images/1060/3536/6c779.png)
With respect to the principle of exponential, we have;
= ![\frac{(-5k^{2}m)(16k^{4} m^{4})(9k^{2}m^{8} }{k^{2}m^{3} }](/tpl/images/1060/3536/9ca7d.png)
Applying the law of indices,
= ![\frac{(-5*16*9)(k^{2+4+2})(m^{1+4+8}) }{k^{2} m^{3} }](/tpl/images/1060/3536/0a5c7.png)
= ![\frac{-720k^{8} m^{13} }{k^{2}m^{3} }](/tpl/images/1060/3536/c8497.png)
= -720
x ![k^{-2} m^{-3}](/tpl/images/1060/3536/2349e.png)
= -720![k^{8-2} m^{13-3}](/tpl/images/1060/3536/d5b4b.png)
= -720![k^{6}m^{10}](/tpl/images/1060/3536/67b84.png)
2. ![\frac{3m}{m^{4} }](/tpl/images/1060/3536/59d34.png)
divide the numerator and denominator with common factor m,
= ![\frac{3}{m^{3} }](/tpl/images/1060/3536/d4f37.png)
This can not be simplified further since there are no more common factors, so that;
=
(or 3
)