Question

How do you simplify `\frac { 30b ^ { 14} } { 45b ^ { 10} }`?

Answer 1

See a solution process below:

Explanation:

First, factor and simplify the constants as:

`(30b^14)/(45b^10) => ((15 xx 2)b^14)/((15 xx 3)b^10) => ((color(red)(cancel(color(black)(15))) xx 2)b^14)/((color(red)(cancel(color(black)(15))) xx 3)b^10) =>`

`(2b^14)/(3b^10)`

Now, use this rule for exponents to simplify the `b` terms:

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

`(2b^color(red)(14))/(3b^color(blue)(10)) = (2b^(color(red)(14)-color(blue)(10)))/3 => (2b^4)/3` or `2/3b^4`