Help with algebra?

Question

A student submits homework in which she writes:3 exponent is 2 x 3 exponent is 3 = 729 and(-3) exponent 2 = -9. What doyou think she did wrong, if anything? What would you advise her to do?

Answer 1

in case 1:

instead of calculating: (3 raised to 2) x (2 raised to 3), she calculated: (3 raised to 2) * (3 raised to 2), because she must have thought that (2 raised to 3) = (3 raised to 2), which is not true.

Then, she must have mixed up her exponent rules while calculating, and must have multiplied the bases, or the 3's to get 9, and mulitiplied the exponents, or the 2's to get 4.

Her result : 9 raised to 4 which gives 729

Solution: just multipliy it out; 3raised to 2 = 9 and 2raised to 3 = 8. 8 x 9 =72. you could do it a couple of other ways but this is the easiest.

Case 2:
when the question asked to evaluate (-3) squared, the student must have squared only the 3 and not the (-) sign

the result: - (3) (3) = -9
this is right ONLY if the question asks for (-3) x (3), but since it doesn't, it's wrong

Solution: it is a rule in integers that (-1) x (-1) = +1
therefore, when squaring (-3), the question means both the 3 and the (-) sign. since the square of (-) is (+), answer is +9.

I know it's really wordy, but i couldn't help myself - hope this helps

Answer 2

Do you mean

3² x 3³ =

or

(3²)(3³) =

9 x 27 = 243

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(- 3)² . .is the same as

(- 3)(- 3) = 9

Multiplying negatives within the parenthesis results in a positive product. The exponent applies to the negative symbol and the 3.

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Additional information

- 3² = . . .is the same as

- (3 x 3) = - 9

The exponent applies to the 3 only.

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