Question

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

Answer 1

`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`