<p>I found this question in Barron's SAT math II </p>
<p>(-1/16)^(2/3)</p>
<p>A -0.25
B -0.16
C 0.16
D 6.35
E The value is not a real number</p>
<p>I just enter the formula into my CASIO fx-9750GII (a graphing calculator very similar to Ti-83) with the a+bi mode for complex number. I get -0.07874506562+0.1363904545i
and choice E seems to be correct.</p>
<p>However, Barron says the correct answer is C
Then, I change a+bi into REAL for complex number. I get 0.1574901312, C is right.</p>
<p>The real problem is that according to Barron, I "must use a+bi mode for SAT Math level 2 test"</p>
<p>I hate this paradox. Which would you choose as the correct answer????</p>
<p>If you are taking Math II you should know just by looking at (-1/16)^(2/3) that the result is a real positive number, and by that you would know that -0.07874506562+0.1363904545i wasn’t the answer.</p>
<p>You are relying too much on your calculator</p>
<p>The answer is C.
First, do you know what the question is asking? It’s asking “What is the cube root of -1/16 squared?”. If you have x^(a/b), it means “The b root of x to the a power.”
Since you’re squaring -1/16, it has to be positive. Whenever you raise a number to an even number power, it’s positive.
Since you’re taking the cube root, it’s real even if it’s negative. If the root is odd, then it’s real even if negative. If the root is even, it’s imaginary if it’s negative.
I’m not familiar with your calculator, but I would get a TI-83 or TI-84. Either you’re entering the number wrong (you’re not since it’s working when you enter it in a different mode) or there’s something wrong with the calculator. If you can’t, don’t use a+bi mode if you’re going to be working with real numbers.</p>