Question

How do you simplify `\frac { 12a ^ { - 2} b ^ { - 4} } { 4a ^ { - 8} b }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression using this rule for exponents:

`a = a^color(red)(1)`

`12/4(a^-2/a^-8)(b^-4/b^color(red)(1)) =>`

`3(a^-2/a^-8)(b^-4/b^color(red)(1))`

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

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

`3(a^color(red)(-2)/a^color(blue)(-8))(b^-4/b^1) =>`

`3a^(color(red)(-2)-color(blue)(-8))(b^-4/b^1) =>`

`3a^(color(red)(-2)+color(blue)(8))(b^-4/b^1) =>`

`3a^6(b^-4/b^1)`

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

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

`3a^6(b^color(red)(-4)/b^color(blue)(1)) =>`

`3a^6(1/b^(color(blue)(1)-color(red)(-4))) =>`

`3a^6(1/b^(color(blue)(1)+color(red)(4))) =>`

`3a^6(1/b^5) =>`

`(3a^6)/b^5`