Why does 4p to the -3rd power equal 4/p to the third power when simplified, and not 1/4p to the third power?

Edit: Nevermind, I think I got it, sort of.

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Excelsior, BS Finance, pursuing degree

Studying:

Completed:
CLEP: Hum. (67), Hist. of U.S. I (74), Hist. of U.S. II (71), Intro. Psych. (69), Intro. Soc. (72), Soc. Sci. and Hist. (74), Western Civ I (72), Western Civ II (70), Am. Lit. (60), Intro. to Educ. Psych. (62), P. of Management (74), P. of Market. (74), Intro. Bus. Law (67), P. of Accounting (60), AmGov (68)
DSST: Ethics in Am. (76), P. of Super.(67), HRM (65), Intro to Bus. (70), MIS (65), P. of Fin (62), M&B (65), P. of Stat. (68)
ECE: OB (B)
TECEP:: IntFin, SecAna

Total Credits: 114

Is 3 to the -2 power positive or negative 9? Why?

__________________
Excelsior, BS Finance, pursuing degree

Studying:

Completed:
CLEP: Hum. (67), Hist. of U.S. I (74), Hist. of U.S. II (71), Intro. Psych. (69), Intro. Soc. (72), Soc. Sci. and Hist. (74), Western Civ I (72), Western Civ II (70), Am. Lit. (60), Intro. to Educ. Psych. (62), P. of Management (74), P. of Market. (74), Intro. Bus. Law (67), P. of Accounting (60), AmGov (68)
DSST: Ethics in Am. (76), P. of Super.(67), HRM (65), Intro to Bus. (70), MIS (65), P. of Fin (62), M&B (65), P. of Stat. (68)
ECE: OB (B)
TECEP:: IntFin, SecAna

Total Credits: 114

it's neither...

the answer would be positive 1/9...
because the negative inverses the 3 to 1/3 and then when you apply the exponent (which is 2) to the 1/3 so...

3^-2 = (1/3)^2 = (1/3)*(1/3) = 1/9

does that help? =]

Could y'all start speaking in English now??

hahaha sorry! =D

let's see if i can translate it better by typing steps:

original problem: 3 to the -2 power aka "3^-2"
1) due to the negative power, you flip the 3 upside down so it becomes 1/3
2) then you apply the exponent to it: 1/3 to the 2nd power
3) 1/3 to the 2nd power is bascially the same thing as 1/3 times 1/3
4) which equals to positive 1/9


does that explanation help? sorry, i wish i could write it out for you on paper b/c i'm sure it'd make more sense than on the computer =]

I think the text has it wrong then...

__________________
Excelsior, BS Finance, pursuing degree

Studying:

Completed:
CLEP: Hum. (67), Hist. of U.S. I (74), Hist. of U.S. II (71), Intro. Psych. (69), Intro. Soc. (72), Soc. Sci. and Hist. (74), Western Civ I (72), Western Civ II (70), Am. Lit. (60), Intro. to Educ. Psych. (62), P. of Management (74), P. of Market. (74), Intro. Bus. Law (67), P. of Accounting (60), AmGov (68)
DSST: Ethics in Am. (76), P. of Super.(67), HRM (65), Intro to Bus. (70), MIS (65), P. of Fin (62), M&B (65), P. of Stat. (68)
ECE: OB (B)
TECEP:: IntFin, SecAna

Total Credits: 114

what does your textbook say?

i'm pretty sure 3 to the -2 power is equal to 1/9 because i checked with my TI-83+ calculator. both equal to 0.1111...does your text have an explanation?

I checked it on my TI-85, got the same answer you did. I can't find it in the text, it's possible I took it out of an equation at some point.

__________________
Excelsior, BS Finance, pursuing degree

Studying:

Completed:
CLEP: Hum. (67), Hist. of U.S. I (74), Hist. of U.S. II (71), Intro. Psych. (69), Intro. Soc. (72), Soc. Sci. and Hist. (74), Western Civ I (72), Western Civ II (70), Am. Lit. (60), Intro. to Educ. Psych. (62), P. of Management (74), P. of Market. (74), Intro. Bus. Law (67), P. of Accounting (60), AmGov (68)
DSST: Ethics in Am. (76), P. of Super.(67), HRM (65), Intro to Bus. (70), MIS (65), P. of Fin (62), M&B (65), P. of Stat. (68)
ECE: OB (B)
TECEP:: IntFin, SecAna

Total Credits: 114