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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. Tags equals, expression, question, sat Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Lobinho Computer Science 0 November 11th, 2015 12:06 PM Anthony.R.Brown Number Theory 1 August 24th, 2013 08:56 AM dtmowns Algebra 3 May 3rd, 2013 07:53 PM mglacy Trigonometry 1 June 3rd, 2012 03:18 PM Chee Algebra 1 November 3rd, 2011 05:56 PM

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