Question

I need to understand the steps and why. ty.
`√(y) ^4`

Answer 1

Answer:
`y^2`

Reason:

A square root represents an exponent of 1/2

So
`√(y) = y^(1/2)`

Raising that to the fourth power gets us this,

`(√(y))^4 = (y^(1/2))^4\\\\ (√(y))^4 = y^((1/2)*4)\\\\ (√(y))^4 = y^(2)\\\\`

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Edit: Here's an alternative route

`(√(y))^4 = (√(y))*(√(y))*(√(y))*(√(y))\\\\ (√(y))^4 = (√(y))^2*(√(y))^2\\\\ (√(y))^4 = y*y\\\\ (√(y))^4 = y^2\\\\`

The first line is possible because raising anything to the 4th power is the same as having 4 copies of it multiplied out (eg: 3^4 = 3*3*3*3 = 81).

Then in the second line, I collected the terms into pairs

By line 3, the square root and squaring exponent cancel each other out. This only works if y is not negative.