Question

How do you multiply and simplify `\frac { 45x } { 5} \cdot \frac { x ^ { 9} } { 9x ^ { 2} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(45/(5 * 9))((x * x^9)/x^2) => (45/45)((x * x^9)/x^2) =>`

`(1)((x * x^9)/x^2) => (x * x^9)/x^2`

Next, use these rules of exponents to multiply the `x` terms in the numerator of the fraction:

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

`(x * x^9)/x^2 => (x^color(red)(1) * x^color(blue)(9))/x^2 => x^(color(red)(1)+color(blue)(9))/x^2 => x^10/x^2`

Now, use this rule of exponents to complete the simplification:

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

`x^color(red)(10)/x^color(blue)(2) => x^(color(red)(10)-color(blue)(2)) => x^8`