Verified answer

Do you mean

(√180)x^13 y^20z^(-4)

or

√(180x^13y^20z^4)?

180 = 9 * 4 * 5

so √180 = 3*2*√5 = 6√5

For the other:

(6 x^6y^10z^(-2)√(5x)

sqrt(180)

= sqrt(36 * 5)

= 6 sqrt(5)

sqrt(x^13)

= sqrt(x^12 * x)

= x^6 sqrt(x)

sqrt(y^20)

= y^10

sqrt(z^-4)

= z^-2

So,

√180x^13y^20z^-4

= 6 sqrt(5) x^6 sqrt(x) y^10 z^-2

= 6 x^6 y^10 z^-2 sqrt(5x)

Remove sqrt sign by writing as a power of 1/2:

[(180)(x^13)(y^20)z^(-4)]^(1/2)

Use the law of indices which says that (a^b)^c = a^(bc):

So we have:

180^(1/2) * x^(13/2) * y^(20/2) * z^(-4/2)

= (sqrt180) [x^(13/2)] [y^10] [z^-2]

= 6sqrt5 [x^(13/2)] [y^10] [z^-2]