Question

How do you simplify #(\frac { 24x ^ { 5} y ^ { 4} } { 3x ^ { - 2} y } )#?

How do you simplify #(\frac { 24x ^ { 5} y ^ { 4} } { 3x ^ { - 2} y } )#?
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Answer #1

#8x ^ { 7}y ^ { 3} #

Explanation:

#(\frac { 24x ^ { 5} y ^ { 4} } { 3x ^ { - 2} y } )#

Remember a fraction is a division.
When you are dividing exponents you subtract them.
Also, remember you can only subtract exponents that are over the same variable.

#(\frac { 24color(red)(x ^ { 5}) color(green)(y ^ { 4}) } { 3color(red)(x ^ { - 2}) color(green)(y) } )#

So... our subtractions here are

#color(red)(x^(5-(-2))=color(red)(x^(5+2))=color(red)(x^7)#

#color(green)(y^(4-1)# #<---# Remember if there is no exponent over the variable it is a #1#
#color(green)(y^(4-1)=color(green)(y^3)#

Now move your subtracted exponents to wherever the LARGER exponent was. In this case #x# and #y# both had the larger exponent in the numerator.

#(\frac { 24color(red)(x ^ { 7}) color(green)(y ^ { 3}) } { 3 } )#

Now make sure you check if the numbers are divisible.
They are...
Let's go ahead and divide them.

#(\frac { 24color(red)(x ^ { 7}) color(green)(y ^ { 3}) } { 3 } )#

#24/3=8#

So...

#8color(red)(x ^ { 7}) color(green)(y ^ { 3}) #

answered by: ceenik
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