Question

How do you simplify `(x^2/4)^4`?

Answer 1

`x^8/256`

Explanation:

You can multiply exponents into the brackets as long as it is multiplying and dividing. DO NOT DO THIS FOR ADDITION AND SUBTRACTION!!

Examples:
In multiplication we, would distribute the exponent by multiplying it. For example, if I had `(x xx2)^2`, I could put this as `(x^(1xxcolor(red)2) xx 2^(1xxcolor(red)2))^cancelcolor(red)2 rArr (x^2 xx 4)`.

Another example: If I had `(x^3 -: y^9)^5`, I could distribute the exponent like this:
`(x^(3*color(red)5) xx y^(4xxcolor(red)5))^cancelcolor(red)(5) rArr (x^15 xx y^20)`

For this question:
`(x^2/4)^4` can be written as `(x^2-:4)^4`

We distribute the exponent:

`(x^(2xx4)-:4^(1xx4)) rArr (x^8 -: 4^4)`

Put it back in numerator/denominator form:

`x^8/4^4`

Expand `4^4`

`=x^8/256`

Answer 2

`((x^2)/4)^4=(x^8)/(256)`

Explanation:

`((x^2)/4)^4`

Apply exponent rule `(a^m)^n=a^(m*n)`

`(x^(2*4))/(4^(1*4))=`

`(x^8)/(256)`