Question

How do you evaluate `5z^ -x` for z=-3 and x=2?

Answer 1

See a solution process below:

Explanation:

First, substitute `color(red)(-3)` for `color(red)(z)` and substitute `color(blue)(2)` for `color(blue)(x)` in the expression from the problem:

`5color(red)(z)^(-color(blue)(x))` becomes:

`5 * color(red)(-3)^(-color(blue)(2))`

Now, use this rule for exponents to eliminate the negative exponent:

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

`5 * color(red)(-3)^(-color(blue)(2)) => 5 * 1/color(red)(-3)^(-color(blue)(-2)) => 5 * 1/color(red)(-3)^(color(blue)(2)) => 5 * 1/9 => 5/9`