1. The whole powers
In first and second, you studied the positive integer powers of natural numbers then of integers and finally of fractions and decimals. Until then the powers were positive.
If we can say, the powers have been “invented” in order to simplify the multiplications.
Instead of writing 2.2.2, write 2³.
In third , we move to the higher speed: Arrive the whole powers, so positive or negative while remaining whole. In future years, powers may be fractional.
Note : The negative exponent tells me that I must take the opposite of the designated expression. Thus for example the exponent -3 tells me that I must take the opposite of the expression and then raise this new expression to the cube. A negative power never indicates that the expression considered is negative but simply that we must go to the opposite!
Review the definitions, properties on page 58 and the exercises that you solved on page 59
Obviously review all the exercises done in class. Rewrite them in the draft, check the answers by comparing them to the answers in the notebook. (That supposes a notebook in order and neat!)
Correction of some exercises on the powers of pages 66 and 67: corr_ex_pages_66_et_67
If you still want other exercises on the powers, go see on the internet. Just introduce ‘exercises on the powers’ and many corrected exercises will be proposed.
2.The square roots.
Introduction: see the sheets distributed in class:
Before solving the exercises below, review everything that has been done in class, the theoretical notions, the meaning of the symbols, the notations. Also do the exercises done in the notebook. Check the solutions by comparing with the solutions of the notebook.
Some small reminders:
- How to simplify the radicals: Simplification_of_radicals
- How to add radicals: Somme_de_radicaux
- How to multiply radicals: Product_of_rounded_rules
- Making the denominators rational: Making_the_national_dominators
Here are some other ex_radical_1 exercises and their corrections. Corr_ex_radicaux
and others: ex_radicaux_2
Duty for the: must_role_carr_e_2006_2007
test example: November 8, 2009 test: test_radicaux_09_10
Correction of exercises on page 70 done in class correction_page_70