Question

If 3/8 power is -5 into 16/21 power is -5 is equals to 2/ 7 power is x find x³​

Answer 1

Answer:

Just saying "adjoin all roots" isn't really going to help in figuring out the degree of the extension.

So you really want to be more explicit.

One root is clearly 3–√8. Another is −3–√8; but these are the only two real roots, and the splitting field is supposed to have 8 roots, so they are not it; you'll certainly need to deal with complex numbers. But you should know what the degree of Q[3–√8] over Q is, which will also get you started with the degrees.

How much do you know about "complex roots of unity"? You want some complex number ζ with the property that ζ8=1. Look up "primitive roots of unity". That should help you continue.

Answer 2

Answer:

x= 10, x=2/7^3

Step-by-step explanation:

3/8 × 16/21

3/8^-5+(-5) 16/21

(3/8×16/21)^10

(2/7)^10