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August 11th, 2019, 07:39 AM  #1 
Newbie Joined: Aug 2019 From: Florida Posts: 1 Thanks: 0  Which Expression Equals SAT Question
I have an SAT practice question stating: Which of the following expressions is equivalent to (4x^3)^2/3? The answer is 2x^2 * 3√2 (or ^2/3, I don't know how to indicate that specifically using keys but the 3 is inside the v of the square root symbol) But my question is how I would multiply that expression to get the answer? Any math calculator or guide I consult seems to say that you can't multiply the expression, but it's clearly happening here. Thank you very much! 
August 11th, 2019, 09:01 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250 
If x is real, $\left(4x^3\right)\!^{2/3} = \left(2^2\!\left(x^3\right)\right)\!^{2/3} = \left((2)^{4/3}\right)\!x^2 = 2\!\left(2^{1/3}\right)\!x^2 = 2\sqrt[\large3]{2}x^2\!$.

August 13th, 2019, 05:15 PM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 673 Thanks: 88 
To show my work without using fractional exponents as much, take the square and then the cube root. The square is 16x^6. To simplify, write it as 2*8x^6. The cube root of 8 is the first part of skipjack's answer, the cube root of 2 is the second part of his answer, and the cube root of x^6 is x^2.


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