Question

here's another question...
(x^-2 / y^0) ^1

I need explanation as I am having difficulty understanding the quotient rule.

Answer 1

Your question is \[\large (\frac{x^{-2}}{y^{0}})^1\]

Answer 2

And here's are some useful tip: Everything ^1 gives the number itself; example: \(x^1=x\)
Negative exponent: \(\LARGE x^{-n}\), n being any constant, \(\LARGE \frac{1}{x^n}\)

Answer 3

And for the quotient rule, it only applies to number that have the \(\color{red}{\text{same}}\) base, \(\LARGE \frac{x^{\alpha}}{x^{\beta}}=x^{\alpha - \beta}\)

Answer 4

Let's go back to your question: there's a negative exponent, \(\large x^{-2}\), we can rewrite this as \(\LARGE \frac{1}{x^2}\)

Also, anything to the 0 power gives 1, for instance \(\large x^0=1\)

Answer 5

So let's solve it already! \[\LARGE (\frac{x^{-2}}{ y^0}) ^1=\frac{x^{-2}}{1}=x^{-2}=\frac{1}{x^2}\]

Answer 6

thanks! I understand it now. So what if the y's power was not zero? What should we have done in that case?

Answer 7

if it were not zero nor negative, then it will remain in the denominator

Answer 8

gotcha!