How do you simplify #(x^6)^3/(x^4)^6#?

1 Answer
Aug 28, 2016

Answer:

#1/x^6#

Explanation:

Using the #color(blue)"laws of exponents"#

#color(orange)"Reminder"#

#• color(red)(|bar(ul(color(white)(a/a)color(black)((a^m)^n=a^mn)color(white)(a/a)|)))#

#rArr(x^6)^3=x^(6xx3)=x^(18)" and " (x^4)^6=x^(4xx6)=x^(24)#

Thus we have #(x^6)^3/(x^4)^6=x^(18)/x^(24)#

#color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)((a^m)/(a^n)=a^(m-n))color(white)(a/a)|)))#

#rArr(x^(18))/(x^(24))=x^(18-24)=x^(-6)#

#color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(a^(-m)=1/(a^m))color(white)(a/a)|)))#

#rArrx^(-6)=1/x^6#
#color(blue)"-------------------------------------------------------------"#

#rArr(x^6)^3/(x^4)^6=(x^(18))/x^(24)=x^(-6)=1/x^6#