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

1 Answer
Nov 9, 2017

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