Question

How do you simplify `(\frac { x ^ { - 4} y ^ { 2} } { x ^ { 5} y ^ { 6} } ) ^ { 2}`?

Answer 1

`(1/(x^18y^8))`

Explanation:

The first thing we should do is multiply each exponent by `2`

`((x^-4y^2)/(x^5y^6))^2 -> ((x^(-4*2)y^(2*2))/(x^(5*2)y^(6*2))) -> ((x^-8y^4)/(x^10y^12))`

What we could do next is rewrite the expression using only positive exponents. You'll notice that `x^-8` is a negative exponent so we have to make positive using this rule: `(a^(-b)=1/a^b)` Basically, we are moving the `x^-8` to the denominator.

This would result in:

`((y^4)/(x^8x^10y^12))`

Finally, we can simply the expression using the following rules:

`x^a*x^b=x^(a+b)`

`x^a/x^b=x^(a-b)`

Thus:

`((y^4)/(x^8x^10y^12)) : x^8*x^10 = x^(8+10) = x^18; y^4/y^12 = 1/(y^8)`

So our final answer is...

`(1/(x^18y^8))`