Question

Simplify 5y^-2

please help fast!!!

Answer 1

`(5)/(y^2)`

Explanation:

So you have the following expression:
`5y^_-2}`

There is no parenthesis, so the -2 exponent is only applied to the y, and not the 5.

To rewrite a negative exponent, you can use the property:
`((a)/(b))^(-x)=((b)/(a))^x`

You can derive this property from the exponent property:
`(x^a)/(x^b)=x^(a-b)`

which essentially consists of just cancelling out the x's from the numerator and the denominator, but in some cases you're "cancelling" out more x's in the denominator, than there are in the numerator.

Take for example:
`(x^2)/(x^5)`, using the quotient of exponents, we can simplify it to:
`x^(2-5)=x^(-3)`

And to see why this happening, let's expand out the fraction:
`(x^2)/(x^5)\implies (x*x)/(x*x*x*x*x)`, as you can see in this fraction there are two x's in the numerator and there are also 2 in the denominator (more than 2, but there are at least 2 in the denominator), thus we can cancel out two of the x's leading to the fraction:
`(1)/(x*x*x)`

So by definition:
`x^(-3)=(1)/(x*x*x)=(1)/(x^3)`

So negative exponents are just the reciprocal in a way, or more formally:
`((a)/(b))^(-x)=((b)/(a))^x`

So in your case specifically we can rewrite y^(-2) as:
`5 * y^(-2)\implies5*(1)/(y^2)\implies (5)/(y^2)`