Can someone answer these algebra 2 questions please?

Question

Evaluate:
1) 5 square root -32
2) 4 square root 625
3) Suppose x is greater than or equal to 0 and 4 (square root) (square root) x^13=x^y. Give the value of y.
4) Suppose m>0. Rationalize the denominator of 6/square root of 2m and simplify.

Please show work. If you answer all questions right, you get best answer points. Thank you!!!

Answer 1

Is it 5*the square root of 32 or 32^(1/5)?
1. (square root of -2)*2i

-32
2 16
2 8
2 4
2 2
or square root of 32=5.65*5=28.28

2. 5
625
125 5
5 25
5 5
or square root of 625=25*4=100
3. (x^13)^(1/4)=(x^y), (2^13)=8192^(1/4)= 9.514=2^(13/4), y=(13/4)
4. s=square root, (6/s2m)*(s2m)/(s2m)=6s2m/2m=3s2m/m
Answer to 4- 3* the square root of 2m/ m

Answer 2

1.) (-32)^1/5 = [(-1)(32)]^1/5 = (-1)^1/5 (32)^1/5 = (-1)(2) = -2.

Proof:
(-2) x (-2) x (-2) x (-2) x (-2) = -32

2.) There are two interpretations for this:

In this interpretation, one extracts the fourth root of 625:
.
625^1/4 = 5

Proof:
5^4 = 5 x 5 x 5 x 5 = 625. Therefore:
625^1/4 = (5^4)^1/4 = 5^(4/4) = 5^1 = 5

or

In this one, the square root of 625 is multiplied by 4:

4√625 = 4 (25) = 100

Proof:
√625 = 25.
4 x 25 = 4 (20 + 5) = 80 + 20 = 100.

3.) Extract the fourth root of x^13 and set it equal to x^y:

(x^13 )^1/4 = (x^y)
(x^13 )^1/4 = x^[(13)(1/4)] = x^(13/4) = x^y, so 13/4 = y.

Proof:
(x^y)^4 = x^4y = [x^(4)(13/4)] =
x^(4/4)(13) = x^(1)^(13) = x^13

4.) 6/square root of 2m = 6 / √(2m)
To rationalize the denominator of a fraction containing a radical we multiply both the numerator and the denominator of the fraction by the denominator. That's the same thing as multiplying the fraction by 1, so we don't change the fraction's value.

[6 / √(2m)][√(2m) / √(2m)] = 6 √2m / (√2m)² =
6 √(2m) / 2m = (2)(3) √(2m) / (2) m =
3 √(2m) / m

Answer 3

(x-2)(x+16) these are the two factors because 16*-2 = -32 ::: and 16+-2 = 14 using the zero product property, you equalize each product to zero. x-2 = 0 x = 2 x+16=0 x=-16

Answer 4

how about asking 4 someone 2 explain the problems 2 u, not do u homework 4 u.

Answer 5

2) 1.4953487812212205
i only know #2

square root= sq

625 sq=25 25sq=5 5sq=2.2360679775 2.2360679775sq=1.4953487812212205

Answer 6

1) 28.284....
2)100
3)Confusing Question
4) No can do. Sorry