How do you simplify `(2x^2y^3)/(8xy^7)`?

To simplify a mathematical expression or equation, we must combine the like terms by performing the required mathematical operation. In our expression, the like terms are: `2` and `8`, `x^2` and `x`, `y^3` and `y^7`.

First, let us divide `2` by `8`. The quotient is `1/4`.
`((2)x^2y^3)/((8)xy^7)`

Now the expression becomes like this. It is not needed to write the `1` down.
`(x^2y^3)/(4xy^7)`

Next, divide `x^2` by `x`. Law of exponents state that "when dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent." In this case, this simply means:
`((x^2)y^3)/(4(x)y^7) => x^(2-1) => x or x/1`

Put the `x` in the numerator. The expression is now like this. Now we are down to our final step.
`(xy^3)/(4y^7)`

Repeat the previous step, only instead, we are now dividing `y^3` by `y^7`.
`(x(y^3))/(4(y^7)) => y^(3-7) => y^-4`
Law of exponents state again that "when a base is raised to a negative power, find the reciprocal of the base, keep the exponent with the original base, and drop the negative." (To find the reciprocal of a fraction, just switch the numerator and denominator!) This means:
`y^-4 or 1/y^4`

Now this is our simplified expression. Hope this helps.
`(x)/(4y^4)`

http://people.sunyulster.edu/nicholsm/webct/WebCT2/laws_of_exponents.htm