simplifying expressions?

Question

(9m)^3/2

(27b)^1/3 / (9b)^-1/2

if x^3/4 = 27, what is the vaule of x?

if b^-1/2 = 4, what is the value of b?

if (2m)^-6 = 16, what is the vaule of 2^3m?


PLEASE HELP?! MY ANSWERS ALWAYS COME UP TO BE LARGE NUMBERS THAT DO NOT FIT.

best answer = 10 points! <3

Answer 1

(9m)^(3/2)
= 3³ m^(3/2)
= 27 m^(3/2)

x = 27^(4/3)
x = 3^4
x = 81

1 / b^(1/2) = 4
b^(1/2) = 1 / 4
b = 1 / 16

1 / (2m)^6 = 16
(2m)^6 = 1 / 16
(2m)^3 = 1 / 4

Answer 2

1. (9m)^3/2 = 27m^3/2 = 27m square root of m

(9^3/2) (m^3/2) = 27m (m^1/2)

2. (27b)^1/3 / (9b)^-1/2 = 9b^5/6

3b^1/3 / (1 / 9b)^1/2
3b^1/3 / (1 / 3b^1/2)
(3b^1/3)(3b^1/2)
(9b^1/3+1/2)
9b^5/6

3. x^3/4 = 27
x = 27^4/3
x = (3^3)^4/3
= 3^4
= 81

4. b^-1/2 = 4
b = 4^-2
b = 1/16

5. (2m)^-6 = 16
your question here is not clear.. i'm not sure if 2m or just m
is raised to -6.

Answer 3

If you are interested in learning how to do these (instead of just getting the answers), here are a few of the rules you should know:
(1) (x^a)*(x^b) = x^(a + b)
(2) (x^a)/(x^b) = x^(a - b)
(3) (x*y)^a = (x^a)*(y^b)
(4) x^(-a) = 1/(x^a)
(5) x^(1/a) = y if and only x = y^a
(6) x^(a/b) = [x^(1/b)]^a
(7) x^2 = x*x, x^3 = x*x*x. ...

Then (9m)^(3/2) = [9^(3/2)]*m^(3/2) by (2)
= {[9^(1/2)]^3}*m^(3/2) by (6)
= {[3]^3}*m^(3/2) by (5)
= 27*m^(3/2) by (7).

Get it?

Answer 4

1) 27m^(3/2)
2) 9b^(5/6)
3) 81
4) 1/16

Answer 5

(1)=27m^3/2
(2)=9b^5/6
(3)x=3^4 or 81
(4)b=4^-2 or1/16
(5)the value=1/4 or 4^-1