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

2 Answers
Oct 29, 2015

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

Oct 29, 2015

((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)