Question

How do you simplify `\frac { a ^ { - 2} b ^ { 6} } { a ^ { 3} b ^ { - 1} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(a^-2/a^3)(b^6/b^-1)`

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))`

`(a^color(red)(-2)/a^color(blue)(3))(b^6/b^-1) => (1/a^(color(blue)(3)-color(red)(-2)))(b^6/b^-1) => (1/a^(color(blue)(3)+color(red)(2)))(b^6/b^-1) => (1/a^5)(b^6/b^-1)`

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

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

`(1/a^5)(b^color(red)(6)/b^color(blue)(-1)) => (1/a^5)(b^(color(red)(6)-color(blue)(-1))) => (1/a^5)(b^(color(red)(6)+color(blue)(1))) =>`

`(1/a^5)(b^7) => b^7/a^5`