SOLUTION: how do you solve this rewriting using a single exponent 32^2y^10? I know the answer is 2y^10 but i dont understand.

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Question 985969: how do you solve this rewriting using a single exponent 32^2y^10? I know the answer is 2y^10 but i dont understand.
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
The answer is not 2y10 but (2y)10.  The parentheses
are ABSOLUTELY NECESSARY!

The secret is what you can do with the number 32:

32 = 16×2 = 8×2×2 = 4×2×2×2 - 2×2×2×2×2 = 25

So

322y10

Now replace the 32 by (25).  Be sure to put the parentheses.

(25)2y10

Remove the parentheses by multiplying the inner exponent 5 by the 
outer exponent 2, getting the exponent 10:

210y10

Now we can use just one 10 exponent by enclosing the 2 and the y 
in parentheses and taking the common 10 exponent out on the right:

(2y)10

It will be wrong if you leave off the parentheses as you did above.

Parentheses are EXTREMELY IMPORTANT throughout algebra.  So try to
learn how to use them properly as they are like putting a rubber band 
around things to hold things together.

 is wrong.   is right. 

The first one is wrong because the 2 would not get raised to the 10th 
power but only the y.   However by putting parentheses around both the 2
and the y, they BOTH get raised to the 10th power.

Edwin
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