Exponent Law Violation?

[marty.fielding]

I am working on a problem from the extra problem set from GMAC for the computer and I am confused with a wrong answer.

The question is "which of the following is equal to 10^-(-3)^2?"

From my understanding of exponent laws, anytime you have an exponent raised to an exponent you multiply, in this case 3*2=6 INSTEAD of performing a standard exponent evaluation 3^2=9.

According to GMAC, my answer of 10^-6 is incorrect with the correct answer being 10^-9. Can anyone help me clarify what I am missing here?

Thanks

[jnelson0612]

I am working on a problem from the extra problem set from GMAC for the computer and I am confused with a wrong answer.

The question is "which of the following is equal to 10^-(-3)^2?"

From my understanding of exponent laws, anytime you have an exponent raised to an exponent you multiply, in this case 3*2=6 INSTEAD of performing a standard exponent evaluation 3^2=9.

According to GMAC, my answer of 10^-6 is incorrect with the correct answer being 10^-9. Can anyone help me clarify what I am missing here?

Thanks

This one is confusing for sure!

You are right that when you have a base with an exponent to another exponent you should multiply the exponents together. So for instance, (10^3)^2 would be 10^6. Notice here, the square is squaring the entire value, base of 10 and exponent of 3.

In this case, the square is only squaring the -3; see how it's NOT squaring the entire expression, including the base of 10? Thus, just square the -3 and then apply the negative and you have 10^-9.

Let me know if this is at all unclear!

[RonPurewal]

marty, note that your notation--"10^(-3)^2"--is ambiguous. (this is particularly notable because it obfuscates the order of operations, which is the entire point here.)

the question is whether it's
(a^b)^c
or
a^(b^c).

if it's the former, then that's the old familiar exponent law.

if it's the latter, then there are no simplification rules (other than to evaluate the numbers, if indeed they are specific numbers). i.e., there's no way to simplify the expression a^(b^c).

generally, if there are no parentheses in the expression--i.e., if all that's written there is a number, then a smaller number, then an even smaller number--then it's the latter of these. it's an arbitrary convention, but convenient. (since (a^b)^c simplifies to a^(bc) anyway, the notation wouldn't have much utility in that case.)

[RonPurewal]

in any case, what's most important is this:
• are there parentheses in the given problem?
• are both options (10^-6 and 10^-9) given?

if the answers are no and yes, then you've a valid complaint here (i wouldn't expect anyone to know this convention, since it's not treated by the usual order-of-operations/PEMDAS protocol).

on the other hand, if only one of the expressions 10^-6 and 10^-9 is actually present in the answer choices, then this is a non-issue.

(note that our forum rules expressly specify that all answer choices be posted... please comply with these rules next time, thanks)