How do you simplify #\frac { 18y ^ { 3} } { 16y ^ { 7} }#?

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Answer 1 · 2017-01-13T21:44:57

See full explanation below:

First, we can simplify the constants/coefficients:

#(18y^3)/(16y^7) -> ((2 xx 9)y^3)/((2 xx 8)y^7) -> ((cancel(2) xx 9)y^3)/((cancel(2) xx 8)y^7) - (9y^3)/(8y^7)#

We can now use this rule for exponents to deal with the #y# terms:

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

#(9y^color(red)(3))/(8y^color(blue)(7)) -> (9y^(color(red)(3)-color(blue)(7)))/8 -> (9y^-4)/8#

Or is we don't want negative exponents we can use this rule for exponents:

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

#(9y^color(red)(3))/(8y^color(blue)(7)) -> 9/(8y^(color(blue)(7)-color(red)(3))) -> 9/(8y^4)#