Question

How do you multiply `\sqrt { 9x ^ { 4} } \cdot 2x ^ { - 3}`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite the expression on the left as;

`sqrt(9)sqrt(x^4) * 2x^-3 =>`

`3x^2 * 2x^-3`

Next, rewrite the expression as:

`(3 * 2)(x^2 * x^-3) =>`

`6(x^2 * x^-3)`

Next, we can use this rule of exponents to multiply the `x` terms:

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

`6(x^color(red)(2) xx x^color(blue)(-3)) => 6x^(color(red)(2) + color(blue)(-3)) => 6x^-1`

If necessary, to eliminate the negative exponent we can use these rules for exponents:

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

`6x^color(red)(-1) => 6 * 1/x^color(red)(- -1) => 6 * 1/x^color(red)(1) => 6 * 1/x => 6/x`