SOLUTION: Why is the largest perfect square factor of 20x^7 4x^6? Specifically, why did the ^7 turn into a ^6? Getting stuck here!

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Question 1118094: Why is the largest perfect square factor of 20x^7 4x^6? Specifically, why did the ^7 turn into a ^6? Getting stuck here!
Found 3 solutions by ikleyn, math_helper, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Why highlight%28cross%28is%29%29 the largest perfect square factor of 20x^7 highlight%28is%29 4x^6? Specifically, why did the ^7 turn into a ^6? Getting stuck here!
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I edited your post in order for it makes sense.


Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+20x%5E7++=+%284x%5E6%29%2A%285x%29+
+4x%5E6+ is a perfect square +4x%5E6+=++%282x%5E3%29%5E2++ and it is the largest one that is a factor of +20x%5E7+

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


4x^6 is a perfect square: (2x^3)^2 = 4x^6.

When you factor 4x^6 out of the original expression 20x^7, what is left is 5x: %2820x%5E7%29%2F%284x%5E6%29+=+5x.

Neither 5 nor x is a perfect square, so 4x^6 is the largest perfect square factor of 20x^7.