Question

How do you solve `x^ { - \frac { 2} { 2} } = \frac { 1} { 729}`?

Answer 1

See a solution process below:

Explanation:

First, evaluate the exponent expression as;

`x^-1 = 1/729`

Next, use these rules of exponents to eliminate the negative exponent and simplify the `x` term:

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

`x^color(red)(-1) = 1/729`

`1/x^color(red)(- -1) = 1/729`

`1/x^color(red)(1) = 1/729`

`1/x = 1/729`

Because both sides of the equation are pure fractions we can flip the fractions to solve for `x`:

`x = 729`