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)`

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

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

`(y^(x-(x)))^4`

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

`(y^(x-x))^4`

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

`(y^0)^4`

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

Therefore, the answer will be `1`

We will use the following rule:

`a^bcdota^c=a^(b+x)`

Hence you have

`(y^xcdoty^(-x))^4=(y^(x-x))^4=(y^0)^4`

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

`(y^0)^4=1^4=1`

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

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now