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

2 Answers
Oct 29, 2015

Answer:

#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

Answer:

#((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)#