SOLUTION: if (4a)^3 = (2a)^2 What is a?

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Question 326523: if (4a)^3 = (2a)^2
What is a?

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
if %284a%29%5E3%22%22=%22%22%282a%29%5E2
What is a?

%284a%29%5E3%22%22=%22%22%282a%29%5E2

Make sure every factor inside each set of parentheses
shows its exponent, even when it is 1:

%284%5E1a%5E1%29%5E3%22%22=%22%22%282%5E1a%5E1%29%5E2

Now remove the parentheses by multiplying each exponent
within the parentheses by the exponent outside the
parentheses:

4%5E%281%2A3%29a%5E%281%2A3%29%22%22=%22%222%5E%281%2A2%29a%5E%281%2A2%29

4%5E3a%5E3%22%22=%22%222%5E2a%5E2

Write 4%5E3 as 64 and 2%5E2 as 4

64a%5E3%22%22=%22%224a%5E2

Get 0 on the right side:

64a%5E3%22%22-%22%224a%5E2%22%22=%22%22%220%22

Factor 4a%5E2 out of the left side:

4a%5E2%22%28%2216a%22%22-%22%221%22%29%22%22%22=%22%22%220%22

Use the zero-factor property to set each factor equal to 0:

 

So there are two solutions.

Edwin