Question

How do you simplify #\frac { 3x ^ { - 2} y ^ { 3} } { 9x ^ { 4} y ^ { 5} }#?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

#3/9(x^-2/x^4)(y^3/y^5) => 1/3(x^-2/x^4)(y^3/y^5)#

Next, use this rule of exponents to simplify the #x# term:

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

#1/3(x^color(red)(-2)/x^color(blue)(4))(y^3/y^5) => 1/3(1/x^(color(blue)(4)-color(red)(-2)))(y^3/y^5) =>#

#1/3(1/x^(color(blue)(4)+color(red)(2)))(y^3/y^5) => 1/3(1/x^(color(blue)(6)))(y^3/y^5) => 1/(3x^6)(y^3/y^5)#

Now, use this same rule to simplify the #y# term:

#1/(3x^6)(y^color(red)(3)/y^color(blue)(5)) => 1/(3x^6)(1/y^(color(blue)(5)-color(red)(3))) => 1/(3x^6)(1/y^2) =>#

#1/(3x^6y^2)#