Properties of Exponents Simplify:  ` (y^x cdot y^(-x))^4`

Expert Answers
kingattaskus12 eNotes educator| Certified Educator

Remove the negative exponent in the numerator by rewriting `y^(-x)`  as `1/(y^x)`  A negative exponent follows the rule: `a^(-n) = 1/(a^n)`

`(y^x * 1/(y^x))^4`

Multiply `y^x`  by `1/(y^x)`   to get `(y^x)/(y^x)`  


Reduce the exponents of y by subtracting the denominator exponents from the numerator exponents.


Multiply `-1` by each term inside the parentheses.


Since x and -x are like terms, add `-x` to `x` to get `0` .


Expand the exponent `(4)` to the expression.

Therefore, the answer will be `1`

tiburtius eNotes educator| Certified Educator

We will use the following rule:


Hence you have


Now since for any `ane0,` `a^0=1` if we assume that `yne0` then you have


So if  `yne0` then `(y^xcdoty^(-x))^4=1`