Question

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

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})`