How do you simplify #\frac { 5x ^ { 0} y ^ { 6} } { 10x ^ { 4} y ^ { 8} }#?

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Answer 1 · 2016-12-23T21:28:40

#1/(2x^4y^2)#

The first simplification we can make is to reduce the constants:

#(5x^0y^6)/(10x^4y^8) -> (5x^0y^6)/((5*2)x^4y^8) -> (color(red)(cancel(color(black)(5)))x^0y^6)/((color(red)(cancel(color(black)(5)))*2)x^4y^8)#

#(x^0y^6)/(2x^4y^8#

Now, we can use one of the rules for exponents to simplify the terms with exponents:

#color(red)(x^a/x^b = 1/x^(b-a))#

Applying this rules gives:

#1/(2x^(4-0)y^(8-6))#

#1/(2x^4y^2)#