Problem Solving

Which of the following is equal to 10^[-(-3)]^2?

a. 1/10^9
b. 1/10^6
c. 1/10^3
d. 10^6
e. 10^9

method of attack:

PEMDAS

1. begin with [-(-3)] = 3
2. so it becomes 10^(3^2)
3. then it becomes 10 ^ 9

Answer: E

I thought A^b^c = A^bc?

fangtray wrote:I thought A^b^c = A^bc?

Here you go:

The parenthesis is important

fangtray wrote:I thought A^b^c = A^bc?

Depends on the parentheses:

(a^b)^c = a^bc

a^(b)^c = a^(b^c)

I see that the parentheses comes first, so we get 10^3^2, but I don't see why this becomes 10^(3^2) instead of (10^3)^2.
The negative of -3 is the only term within brackets, so both the "10^" and "^2" operations are outside of the term in parentheses/brackets.
With operations at the same level, doesn't the first such operation - reading from left to right - occur first?

Bill@VeritasPrep wrote:

fangtray wrote:I thought A^b^c = A^bc?

Depends on the parentheses:

(a^b)^c = a^bc

a^(b)^c = a^(b^c)

what if there were no parenthesis...we've worked on many problems where simplying the exponent was just to multiple it..

for example a^b^c 2^3^4 = 2^81? or 2^12..

how am i just finding out about this now..haha... i've done like so many problems involving simplifying exponents and multiplying the exponents was right, and i've ALWAYS multiplied the exponents in the problems.. i think this is the first problem i've come across that requires me to do it differently.