Question

how do you do the following without a calculator:

3 x 4^(1/4) - 12 x 2^(-3/2)

Answer 1

solve for the unknown:

6e^(-4t) = 2

Answer 2

ahh sorry that was supposed to be a separate question.

Answer 3

note that you can combine exponents if they have the same base. thus, we change the 4 (first term) to 2^2 since the base on the second term is equal to 2:
3 x 4^(1/4) - 12 x 2^(-3/2)
3 x (2^2)^(1/4) - 12 x 2^(-3/2)
also, since 12 = 2*2*3 = (2^2)*3,
3 x (2^2)^(1/4) - (3*2^2) x 2^(-3/2)
3 x 2^(1/2) - 3 x (2^2) x (2^(-3/2))
note that to multiply exponents, first they must have the same base, and then you can add their exponents. thus, for the second term, we just add the exponents of 2:
3 x 2^(1/2) - 3 x (2^2) x (2^(-3/2))
3 x 2^(1/2) - 3 x (2^(2 - 3/2))
3 x 2^(1/2) - 3 x 2^(1/2)
0

hope this helps~ :)

Answer 4

thank you! :]