Question

How do you simplify `(3x^-2y^2)/(6xy^2)`?

Answer 1

`1/(2x^3)`

Explanation:

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

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(a^nxxa^m=a^(n+m)" and " a^-mhArr1/a^m)color(white)(a/a)|)))`

`rArr(3x^-2y^2)/(6xy^2)" can be expressed as"`

`3/6xxx^-2/x xxy^2/y^2`

`=cancel(3)^1/(cancel(6)^2)xx1/x^(1+2)xx(cancel(y^2)^1)/cancel(y2)^1`

`=1/2xx1/x^3xx1=(1xx1xx1)/(2xxx^3xx1)=1/(2x^3)`