SOLUTION: Hi, A number to the 7th power divided by the same number to the 3rd power equals 256. What is the number? I was able to get x^4=256, but have no idea how do go any further. Ple

Algebra ->  Exponents -> SOLUTION: Hi, A number to the 7th power divided by the same number to the 3rd power equals 256. What is the number? I was able to get x^4=256, but have no idea how do go any further. Ple      Log On


   

Question 228346: Hi,
A number to the 7th power divided by the same number to the 3rd power equals 256. What is the number?
I was able to get x^4=256, but have no idea how do go any further. Please help. Thank you.
Mel
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Here's a couple of ways:
  1. Direct. Try raising numbers to the fourth power and see if you can get 256.
    • 2%5E4+=+2%2A2%2A2%2A2+=+16
    • 3%5E4+=+3%2A3%2A3%2A3+=+81
    • 4%5E4+=+4%2A4%2A4%2A4+=+256 Bingo!
    The problem with approach is that you tend to forget the "other" number. -4 works, too!
  2. Solve by factoring:
    1. Subtract 256 from each side:
      x%5E4-256=0
    2. Factor. This is a difference of squares:
      %28x%5E2%2B16%29%28x%5E2-16%29+=+0
      We still have a difference of squares:
      %28x%5E2%2B16%29%28x%2B4%29%28x-4%29+=+0
    3. Solve. In order for the product to be zero one of the factors must be zero. So:
      x%5E2%2B16+=+0 or x+%2B4+=+0 or x-4+=0
      The first equation is impossible (i.e. no solution) because you can't square something, add 16 and end up with zero. (Think about it.) But the other two equation can be solved:
      x+=+-4 or x+=+4
      This way takes a little more work but you are less likely to overlook the -4.