There are two numbers whose 400th powers are equal to 9^1000. In other words, there are two numbers that can replace x in the equation x^400 = 9^1000 making the equation true. What are those numbers? Explain the process by which you got your answer.
x400 = 91000
Take the 200th root of both sides of the equation.
x400200 = 91000200
x2 = 95
Take the ± sqrt of both sides. (We could have taken the 400th root of both sides to start with.)
x = ±√95
Rewrite 95 as 310
x = ±√310
x = ±35
x = ±243
Well....since it looks as though we're all at the same picnic.....here's my attempt at a weak answer
x^400 = 9^1000
Take the GCF of 400, 1000 = 200 ....so we can write
(x^2)^200 = (9^5)^200 take the 200th root of both sides
(x^2) = 9^5 and we can write
(x^2) = (3^2)^5
x^2 = 3^10 take both roots
x = ± √[3^10] = ± [ 3] ^(10/2) = ± [3]^5 = ± 243