SOLUTION: Arrange the following numbers in increasing order (smallest first, biggest last): A = 2^(1/2)*4^(1/6)*8^(1/3) B = 12*128 C = 8^(1/5)^2*8^(1/5)^3 D = 4*(-1)*2*(-1)*8*(-1

Algebra ->  Square-cubic-other-roots -> SOLUTION: Arrange the following numbers in increasing order (smallest first, biggest last): A = 2^(1/2)*4^(1/6)*8^(1/3) B = 12*128 C = 8^(1/5)^2*8^(1/5)^3 D = 4*(-1)*2*(-1)*8*(-1      Log On


   

Question 1209102: Arrange the following numbers in increasing order (smallest first, biggest last):
A = 2^(1/2)*4^(1/6)*8^(1/3)
B = 12*128
C = 8^(1/5)^2*8^(1/5)^3
D = 4*(-1)*2*(-1)*8*(-1)
E = 2^(1/2)*3*4^(1/4)
Found 3 solutions by ikleyn, mccravyedwin, MathTherapy:
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.

I think that every person should care about his/her brain/mind and time
and do not perform such idiotic assignments by hands.

It is much better to spend your time for some more educative reading,
studying, exercising, walking, sleeping etc.



Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!
Type them all into a TI-84 calculator, just as they're written,
press ENTER and arrange them in increasing order.

Edwin

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Arrange the following numbers in increasing order (smallest first, biggest last):

A = 2^(1/2)*4^(1/6)*8^(1/3)

B = 12*128

C = 8^(1/5)^2*8^(1/5)^3

D = 4*(-1)*2*(-1)*8*(-1)

E = 2^(1/2)*3*4^(1/4)

This, I’m certain, is testing one’s knowledge of the Laws of Exponents, specifically when it comes to CHANGING INTEGERS
to EXPONENTIAL EXPRESSIONS, as well as SIMPLIFYING same-base exponential expressions, down to a MONOMIAL.

So, A = 2^(½) * 4^(1/6) * 8^(1/3) = 2%5E%281%2F2%29+%2A+%282%5E2%29%5E%281%2F6%29+%2A+%282%5E3%29%5E%281%2F3%29 =  = matrix%282%2C1%2C+%22+%22%2C+2%5E%281%2F2%29+%2A+2%5E%282%2F6%29+%2A+2%5E1%29 = matrix%282%2C1%2C+%22+%22%2C+2%5E%283%2F6+%2B+2%2F6+%2B+6%2F6%29%29 = highlight%28matrix%282%2C1%2C+%22+%22%2C+2%5E%2811%2F6%29%29%29
    B = 12*128 = 3(4)(128) = 3%282%5E2%29%282%5E7%29 = 3%282%5E%282+%2B+7%29%29 =  
    C = 8^(1/5)^2 * 8^(1/5)^3 = %288%5E%281%2F5%29%29%5E%28%282+%2B+3%29%29 = matrix%282%2C1%2C+%22+%22%2C+8%5E%28%281%2F5%29++%2A++5%29%29 = 8%5E1 = 8 = highlight%282%5E3%29
    D = 4*(-1)*2*(-1)*8*(-1) = - 64 = highlight%28-+%282%5E6%29%29
    E = matrix%282%2C1%2C+%22+%22%2C+2%5E%281%2F2%29%2A3%2A4%5E%281%2F4%29%29 = matrix%282%2C1%2C+%22+%22%2C+2%5E%281%2F2%29+%2A+4%5E%281%2F4%29+%2A+3%29 = matrix%282%2C1%2C+%22+%22%2C+2%5E%281%2F2%29+%2A+%282%5E2%29%5E%28%281%2F4%29%29+%2A+3%29 = matrix%282%2C1%2C+%22+%22%2C+2%5E%281%2F2%29+%2A+2%5E%282+%2A+%281%2F4%29%29+%2A+3%29 = matrix%282%2C1%2C+%22+%22%2C+2%5E%281%2F2%29+%2A+2%5E%281%2F2%29+%2A+3%29 = matrix%282%2C1%2C+%22+%22%2C+2%5E%28%281%2F2%29+%2B+%281%2F2%29%29+%2A+3%29 = matrix%282%2C1%2C+%22+%22%2C+2%5E1+%2A+3%29 = highlight%28matrix%281%2C3%2C+2%2C+%22%2A%22%2C+3%29%29
                We now have:  

In ASCENDING order, this is: