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

1 Answer
Feb 6, 2017

Answer:

The simplified expression is #(x)/(4y^4)#.

Explanation:

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