### Chap 2: Real Numbers - Spot the Common Mistakes (II)

Revision Exercise 2 (p52 of Textbook) No. 7(b)

1. It should not be (-2)^3+(-7)^3 because it is not the same as (-2+(-7))^3

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4. it is not (-2)^3+(-7)^3 because the answer of the sum is not equivalent to (-2+(-7))^3

5. The working in the Big brackets should be done first. Then it would become (-9)^3=-729

6. The working should be within the bracket first
(-9)^3=-729

7. (-2)^3 + (-7)^3 is not the same as (-9) X (-9) X (-9). The answer should be (-729).

8. It should be (-9)^3
=(-9 x -9 x -9)
=(-729)

9. it should be [-2-(-7)]^3 and not (-2)^3+(-7)^3 because (-2)^3+(-7)^3 is different from [-2-(-7)]^3

(-2)^3+(-7)^3=-351

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11. The correct working should be:
[-2+(-7)]^3
=[-2+(-7)]x[-2+(-7)]x[-2+(-7)]
=(-9)(-9)(-9)
=81x(-9)
=(-729)

12. [-2 + (-7)]^3 is not the same as (-2)^3 + (-7)^3
in (-2)^3 + (-7)^3, it means multiplying then adding. but the numbers are inside the bracket [-2 + (-7)]^3 and the we should do the working inside the bracket first.
so the correct working is:
[-2 + (-7)]^3
= -9 x (-9) x (-9)
= -81 x (-9)
= -729

13. The person who did this should work out the -2+(-7) first. Then it should be okay and the answer should be (-9)(-9)(-9)= (-729)

14. =(-2+(-7))x(-2+(-7))x(-2+(-7))
=(-9)x(-9)x(-9)
=-729

15. [-2+(-7)]^3
= (-9)^3
= 729

16. (-2+(-7))^3
=(-9)^3
=-729 (Ans)

17. [-2+(-7)]^3
=-9^3
-729

18. The working in the bracket should be done first
[-2-(-7)]^3=-729

19. The working is wrong.
( -2+(-7) )^3
=(-2)^3 + (-7)^3
=-8 + (-393)
= -351(Ans)

It should be...
( -2+(-7) )^3
=(-9)^3
= -729(Ans)

20. It should be [-2-(-7)]^3 as [-2-(-7)]^3 is different from (-2)^3+(-7)^3

[-2+(-7)]^3
=[-2+(-7)]x[-2+(-7)]x[-2+(-7)]
=(-9)(-9)(-9)
=81x(-9)
=(-729)

21. The workings in the outer brackets must be done first.After that, take(-9)^3which will give you -729

(-2+-7)^3
=-9^3
=729

23. The workings in the first brackets should be solved first. So,(-2+(-7))=-9. (-9)^3= -729

24. We should work out the (-2+(-7)) first and then (-9)(-9)(-9)so the answer is -729.

25. It should not be (-2)^3 + (-7)^3 as it is totally different from [-2+(-7)]^3.

It is (-2+(-7) raised to the power of 3 and not the sum of the individual integers as in (-2+(-7), it is raised to the power of 3 after they are added.

Therefore, the method is:

[-2+(-7)]^3
= (-9)^3
= -729

-Christopher Nah

26. [-2+(-7)]^3
=[-2=(-7)][-2=(-7)][-2=(-7)]
=-729

27. All of you are right! We should do what's in the bracket first since the power 3 is outside the bracket. Some of you explained pretty well :D

The following presentations needs to be improved on:
1. Some of you put down answer as (-729).
If it is the final answer, we should not write the () any more. So, answer should be written as -729

2. Second line of Darryl's working:
=[-2=(-7)][-2=(-7)][-2=(-7)]