Question

How do you multiply and simplify `\frac { 5v } { 5v ^ { 8} \cdot v \cdot v }`?

Answer 1

See the entire solution process below:

Explanation:

First, cancel common terms in the numerator and denominator:

`(5v)/(5v^8 * v * v) => (color(red)(cancel(color(black)(5)))color(green)(cancel(color(black)(v))))/(color(red)(cancel(color(black)(5)))v^8 * color(green)(cancel(color(black)(v))) * v) => 1/(v^8 * v)`

Now, use these two rules of exponents to multiply the terms in the denominator:

`a = a^color(blue)(1)` and `x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`1/(v^8 * v) => 1/(v^color(red)(8) * v^color(blue)(1)) = 1/v^(color(red)(8)+color(blue)(1)) = 1/v^9`