simplify the expression, express radical expressions?

Question

Theres 3 sections here i dont understand. Im not very good at math and this is over my head.

Simplify the following expressions by performing the indicated operations-
1. 3 (sqrt) x * 3 (sqrt) x
2. (sqrt) t * (sqrt) t
3. 3 (sqrt) R / 3 (sqrt) x

Express each of the following radical expressions using fractional exponents.
1. 4 (sqrt) x^2
2. (sqrt)t
3. 4 (sqrt) x^7
4. 1 / 5(sqrt) x^2

write these using only positive exponents (no signs inbetween except on #1 and #4 (division)
1. x^2 / y^-3
2. x^3 y^-5
3. x^2 y^-4 z^4
4.x^2 / y^-1/2
5. x^2 y^3 t^-4 z^-6 w

Answer 1

sqrt(x) * sqrt(x) = x

1. 9x
2. t

sqrt(x) = x^(1/2)
1.4x
2. t^1/2
3. 4 x^(7/2)

x^(-n)= 1/(x^n) and 1/x^(-n) = x^n

1. x^2y^3
2. x^3y^5

Answer 2

Okay, here goes nothing:

Section 1:

1. 3sqrtx * 3 sqrtx = 9x (sqrt * sqrt eliminates the sqrt)
2. sqrt t * sqrt t = t
3. 3 sqrt R / 3 sqrt x = sqrt R / sqrt x

Section 2:

1. 4 sqrt x^2 = 4x (1/2*2 = 1)
2. sqrt t = t^1/2
3. 4 sqrt x^7 (similar to 1: 1/2 * 7 = 7/2) so 4x^7/2
4. 1/ 5sqrt x^2 = 1/5x

Section 3:
1. x^2 / y^-3 = x^2 y^3 (you put a 1 over y then bring it up)
2. x^3 y^-5 = x^3/y^5
3. x^2y^-4z^4 = x^2z^4 / y^4
4. x^2 / y^-1/2 = x^2 y^1/2
5. x^2 y^3 t^-4 z^-6 w = x^2 y^3 w / t^4 z^6

Move negative exponents to the denominator

Hope this helps.

Answer 3

9x the sqare of a sqare root is always what you have under the radical

t

sqrt(R/x)
4x
simply that, t^1/2
(4x^3sqrtx because x^3 squared is x^6 and that leaves an x under the radical

x/5

x^2y^3
x^3y^5
(x^2z^4))/y^4
x^2y^1/2
(x^2y^2w)/(t^4z^6 )

Answer 4

the trick to those is to in user-friendly terms save dividing stuff with the help of regularly occurring squares consisting of four,9,sixteen,25 and so on until eventually you get an entire answer rt(54xy^4) rt[9(6)x(y^2)^2] 3y^2rt[6x] 3*rt[16x^5] 3*rt[2^3x^2x^3] 2x(3*rt[x^2]