ciyates Posted October 17, 2011 Share Posted October 17, 2011 I am so confused by this and it should be simple. The problem is 4 times the cube root of 81. The answer is 4 x 9 2/3 (2/3) is up like an exponent. Thanks! Quote Link to comment Share on other sites More sharing options...
5of5 Posted October 17, 2011 Share Posted October 17, 2011 (edited) 4*(81)^(1/3) = 4*(9*9)^(1/3) =4*(9^2)^(1/3) =4*(9)^(2/3) The main thing is that 81 is 9 squared, and if you have 9 squared raised to the 1/3 power, you multiple the exponents to get 2/3 (2 times (1/3)). ETA: I would have been tempted to write it as 12*(3)^(1/3) instead! Edited October 17, 2011 by 5of5 Quote Link to comment Share on other sites More sharing options...
creekland Posted October 17, 2011 Share Posted October 17, 2011 (edited) Do the directions tell you to simplify (as opposed to solve)? 9^(2/3) = cube root of 81 = 81^(1/3) Whenever you have a fraction as an exponent, the numerator (top) tells you to raise the base (number) to that power. The denominator (bottom) tells you to take the root of the base. So, 9^(2/3) means 9 squared (or 81), then take the cube root of it. You could take the cube root of 9, then square the answer too. Since the cube root of 81 = 81^(1/3), then 81 factors into (9X9)^(1/3) or 9^(2/3) What you CAN'T do is take 4 X 9 and get 36, then take 36 ^(2/3) or anything similar to it. Exponents come before multiplication in our order of operations. Edited to add that completely factored it should be 2X2 x 3^(4/3) or 2x2x3 x 3^(1/3) - hence the question about the directions to start with. Edited October 17, 2011 by creekland Quote Link to comment Share on other sites More sharing options...
kiana Posted October 17, 2011 Share Posted October 17, 2011 A bit of an addition to 5of5's answer, which is correct. We tend to use ^ for exponentiation on a computer, so x^2 would be x squared. You need to know that the cube root is the same as the 1/3 power. (This is true because when you take a^(1/3) and cube it, you get a^(3/3) which is 1. Remember when you take a power to a power, you multiply the powers. ) So since 81 is 9^2, the cube root of 81 is (9^2)^(1/3), and multiplying the powers gives 9^(2/3). BTW, I have no idea why they've chosen 9 as the base instead of 3 -- I would have written 3^(4/3) instead, and then simplified it to 3*3^(1/3). But hey. Quote Link to comment Share on other sites More sharing options...
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