-5^4 vs. (-5)^4?

Question

I remember doing a practice problem that tested this distinction (or lack thereof), but cannot seem to find the problem. If the GMAT gives you -3^4 + -2^4=? , for example, then what is the answer?

lebron23Goat · Answer

gmat will always give parenthesis. if they dont, then use PEMDAS. -3^4 + -2^4=? = -81+ -16= -97

ccooley · Answer

They're testing the order of operations here. In the case of -3^4, you can think of the '-' as being sort of like multiplying by -1. (That's all a negative sign really means, after all).  E xponents come before  M ultiplication in the PEMDAS order, so you deal with the exponent first,  then  make the whole thing negative. That gives you -81.

If you had (-3)^4, you'd do what was inside of the  P arentheses first. So, you'd 'multiply by -1' and end up with -3. Then, you'd take the whole thing inside of the parentheses, and apply the  E xponent. A negative number, raised to an even power, turns positive. So the answer here would be 81.

Your specific example is worded a little bit oddly, though. It would be unusual to have something like "-3^4 + -2^4", because it appears as if there's a + and then a - right in a row. That would be a little like asking "What is 2 + -4 - -6?". The GMAT might do it, but I don't think I've seen anything quite like that. It would be more common for them to write "-3^4 - 2^4", and the answer there would be -97.

-5^4 vs. (-5)^4?

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