how to solve this equation?

Question

(1/4)k^(1/2)*l^(-1/3) / (1/2)k^(-1/2)*l^(1/4)

MTRS =MPL/ MPK
MPL = (1/4) k^(1/2) l ^(-3/4)
MPK = (1/2) k ^(-1/2) l ^(1/4)
therefore, i got this
(1/4)k^(1/2)*l^(-1/3) / (1/2)k^(-1/2)*l^(1/4)
but i don't know how to go on
how do i cancel them out or solve them

Answer 1

maybe "simplify" would describe the desired goal better>

(1/4)k^(1/2)*l^(-1/3) / (1/2)k^(-1/2)*l^(1/4) = [[ here getting rid of the "/" operator and adding "*" for multiplication:

(1/4) * k^(1/2) * l^(-1/3) * (2) * k^(1/2) * l^(-1/4) =

.. grouping factors via 'associative' & 'commutative' properties:

(1/4) * (2) * k^(1/2) * k^(1/2) * l^(-1/3) * l^(-1/4) =

.. properties of exponents ..
(1/2) * k^((1/2)+(1/2) ) * l^((-1/3)+(-1/4)) =

arithmetic
(1/2) * k^(1) * l^(-7/12) =

arithmetic
(1/2) * k * I^(-7/12)

... or ...
k/(2 * I^(7/12))

.. as an alternate form of 'simplified' expression

which is correct unless I made a 'typing at teh keyboard' mistake

Answer 2

= 1

Answer 3

((1/4)(k^(1/2))(l^(-1/3)))/((1/2)(k^(-1/2))(l^(1/4)))
((1/4)/(1/2)) * k^((1/2) - (-1/2)) * l^((-1/3) - (1/4))
((1/4)*(2/1)) * k^((1/2) + (1/2)) * l^((-1/3) + (-1/4))
(2/4) * k^1 * l^((-4/12) + (-3/12))
(1/2) * k * l^(-7/12)
k/(2l^(7/12))

Answer 4

k/2*l^(7/12)

Answer 5

((k^1/2)(I^-1/3)/4)/(k^-1/2)(I^1/4)/2

=(k/2)/(I^1/3)(I^1/4)

=k/(2)(I^7/12)

Answer 6

Define solve, solve in terms of what? This is not an equation, it's not equal to anything.

Answer 7

zero is fun to try even if it is not an equation.

Answer 8

this equation has nothing to do with anything