Question

Simplify the following expression

Simplifying expressions
8th grade math
Algebra 1

Can someone explain why
(-5k^2m)(2km)^4(3km^4)^2
——————————————
k^2m^3
Simplifies to -720k^6m^10

But 3m/m^4 simplifies to 3/m^2
Even though their both fractions how come only one stays a fraction? What’s the difference so I can figure out in the future?

Answer 1

1.
`((-5k^(2)m)(2km)^(4) (3km^(4)) ^(2))/(k^(2)m^(3))` = -720
`k^(6)m^(10)`

2.
`(3m)/(m^(4) )` =
`(3)/(m^(3) )` (or 3
`m^(-3)`)

Explanation:

1. The given expression is:

`((-5k^(2)m)(2km)^(4) (3km^(4)) ^(2))/(k^(2)m^(3))`

With respect to the principle of exponential, we have;

`((-5k^(2)m)(2^(4)k^(4) m^(4))(3^(2)k^(2)m^(8)))/(k^(2) m^(3) )` =
`((-5k^(2)m)(16k^(4) m^(4))(9k^(2)m^(8) )/(k^(2)m^(3) )`

Applying the law of indices,

=
`((-5*16*9)(k^(2+4+2))(m^(1+4+8)) )/(k^(2) m^(3) )`

=
`(-720k^(8) m^(13) )/(k^(2)m^(3) )`

= -720
`k^(8)m^(13)` x
`k^(-2) m^(-3)`

= -720
`k^(8-2) m^(13-3)`

= -720
`k^(6)m^(10)`

2.
`(3m)/(m^(4) )`

divide the numerator and denominator with common factor m,

=
`(3)/(m^(3) )`

This can not be simplified further since there are no more common factors, so that;

`(3m)/(m^(4) )` =
`(3)/(m^(3) )` (or 3
`m^(-3)`)