Question

How do you multiply `x^ { 0} y ^ { \frac { 1} { 2} } \cdot ( x ^ { 0} y ^ { \frac { 1} { 2} } ) ^ { 2}`?

Answer 1

`ysqrt(y) = y^(3/2) = sqrty^3`

Explanation:

Anything to the power of `0` equals 1. `n^0=1`

A number to the power of `1/2` is the square root of that number. `n^(1/2)=root(2)(n^1)=sqrt(n)`

Raising something with an exponent to another power means multiplying the powers.
`(x^0)^2=x^(0*2)=x^0=1`
`(y^(1/2))^2=y^(1/2*2)=y^1=y`

Now we have: `sqrty*y = y^(1/2) *y = y^(3/2)`

`y^(3/2) = sqrty^3`