SOLUTION: How do you solve (2x+3)^3/4-3=5

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Question 273622: How do you solve (2x+3)^3/4-3=5
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%2B3%29%5E%283%2F4%29-3=5
First let's isolate the base and its exponent by adding 3 to each side:
%282x%2B3%29%5E%283%2F4%29+=+8
If we really understand exponents well we'll see a fairly quick solution to this. We want the exponent on the left to disappear. The quickest way to do this is to raise each side to the 4/3 power. (If you don't see why, wait until we're done:
%28%282x%2B3%29%5E%283%2F4%29%29%5E%284%2F3%29+=+%288%29%5E%284%2F3%29
By our rule for raising powers to a power, we multiply the exponents on the left and when we multiply reciprocals like 3/4 and 4/3 we get... 1!
2x%2B3+=+%288%29%5E%284%2F3%29
On the right side we can use our calculators if we don't get how easy 8%5E%284%2F3%29 is to find by hand. %288%29%5E%284%2F3%29+=+%288%5E%281%2F3%29%29%5E4+=+%28root%283%2C+8%29%29%5E4+=+2%5E4+=+16 So now we have:
2x+%2B+3+=+16
This is simple to solve.
2x+=+13
x+=+13%2F2