Question

How do you simplify `\frac { - 15a ^ { 5} b ^ { - 5} } { 55a ^ { - 2} b ^ { 3} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`-15/55(a^5/a^-2)(b^-5/b^3) =>`

`(5 xx -3)/(5 xx 11)(a^5/a^-2)(b^-5/b^3) =>`

`(color(red)(cancel(color(black)(5))) xx -3)/(color(red)(cancel(color(black)(5))) xx 11)(a^5/a^-2)(b^-5/b^3) =>`

`-3/11(a^5/a^-2)(b^-5/b^3)`

Next, use this rule of exponents to simplify the `a` term:

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

`-3/11(a^color(red)(5)/a^color(blue)(-2))(b^-5/b^3) =>`

`-3/11(a^(color(red)(5)-color(blue)(-2)))(b^-5/b^3) =>`

`-3/11(a^(color(red)(5)+color(blue)(2)))(b^-5/b^3) =>`

`-3/11(a^7)(b^-5/b^3) =>`

`-(3a^7)/11(b^-5/b^3)`

Now, use this rule of exponents to complete the simplification of the `b` term:

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

`-(3a^7)/11(b^color(red)(-5)/b^color(blue)(3)) =>`

`-(3a^7)/11(1/b^(color(blue)(3)-color(red)(-5))) =>`

`-(3a^7)/11(1/b^(color(blue)(3)+color(red)(5))) =>`

`-(3a^7)/11(1/b^8) =>`

`-(3a^7)/(11b^8)`