Question

A quantity representing how many times the base is multiplied by itself

Answer 1

Let suppose the quantity be
`x^(y)` where x=Base, y=exponent

Now, if the base is multiplied by itself

i.e ,
`x * x=x^(2)`

If we raise the power of base multiply by itself by y/2, then it becomes equal to the quantity given.

`[x^(2)]^{(y)/(2)}=x^(y)=Quantity`

Or if we raise the power of quantity by 2/y , then it becomes equal to base multiply by itself.

`[x^(y)]^{(2)/(y)}= x^(2)`

Quantity=
`x^(y)=[base* base]^{(y)/(2)}=[x^(2)]^{(y)/(2)}`