Unité 2: Les Puissances et Les Exposants - Notes

Unité 2: Les Puissances et Les Exposants

Multiple Choice Questions

  1. Write (\frac{c}{c}) as a single power.
    The correct answer should be selected from the options provided (a, b, c, d).

  2. Evaluate:
    The expression to evaluate is not provided. The options are:
    a. -35
    b. 35
    c. 78 125
    d. -78 125

  3. Identify the negative result(s) from the following:
    i)
    ii)
    iii)
    The correct answer should be selected from the options provided:
    a. i et ii
    b. ii et iii
    c. i
    d. i et iii

  4. Evaluate:
    The expression to evaluate is not provided. Options are:
    a. 0
    b. 1
    c. –13
    d. –1

  5. Evaluate:
    The expression to evaluate is not provided. Options are:
    a. -324
    b. 324
    c. -36
    d. -18

  6. Evaluate:
    The expression to evaluate is not provided. Options are:
    a. –31
    b. 57
    c. 20
    d. 41

  7. Simplify to a single power: (\frac{5^8 \times 5^6}{5^{12}})
    a. 5^{26}
    b. 5^2
    c. 5^{14}
    d. 5^4

  8. Evaluate:
    The expression is (\frac{11111112}{O - ~ L G s & O E ya = ( -29 49 - 1 -8)})
    a. -3
    b. -1
    c. 3
    d. 1

Computations

  1. Fill in the table.
PuissanceBaseExposantMultiplication répétée
-7
5^3

  1. Describe the errors in the work shown below AND show the correct solution for this problem: (\frac{5^2 +3 \times 4^2 -3^2}{3^2 - 5\times 4^0})

    Incorrect solution:
    (\frac{25+3 \times 16-9}{9-5} = \frac{28 \times 7}{4} = \frac{196}{4} = 49)

  2. What operation would you do first to evaluate (\frac{3}{5x5x5} + \frac{3^4}{3x3x3x3} + \frac{773}{6565})?
    The student's response indicates "mustiplier premier", which translates to "multiply first".

Priority of Operations and Powers

  1. Use the priority of operations to evaluate the following expression:
    {4^2 - (-5) + 2 \times (-3)^4 + \frac{3^2}{2^3}}

    • Step 1: Evaluate exponents: \Rightarrow 16 - (-5) + 2 \times 81 + \frac{9}{8}
    • Step 2: Multiplication: \Rightarrow 16 - (-5) + 162 + \frac{9}{8}
    • Step 3: Addition and Subtraction (from left to right): \Rightarrow 16 + 5 + 162 + \frac{9}{8} = 183 + \frac{9}{8} = 183 + 1.125 = 184.125

  2. Write 48065 using powers of 10.
    (4 \times 10^4) + (8 \times 10^3) + (0 \times 10^2) + (6 \times 10^1) + (5 \times 10^0)
    (4 \times 10^4) + (8 \times 10^3) + (6 \times 10) + 5

  3. Write (5\times 7)^4 as a product of powers. DO NOT EVALUATE.
    5^4 \times 7^4

  4. Simplify each parenthesis to a single power, then evaluate:
    (\frac{2^5}{2^2})^4 + (3^1 \times 3^3)^2

    • Simplify inside the parenthesis:
      (2^{5-2})^4 + (3^{1+3})^2
      (2^3)^4 + (3^4)^2
    • Apply the power of a power rule:
      2^{3\times 4} + 3^{4 \times 2}
      2^{12} + 3^{8}
    • Evaluate:
      4096 + 6561 = 10657

  5. Jada places tiles on her kitchen floor, which measures 5m by 5m. She bought tiles that cost $90/m^2$. It costs $58/m^2$ for installation. Jada has a coupon for a 30% discount on the installation. If 90 \times 5^2 + 58 \times 5^2 \times 0.70 represents the cost in dollars to place the tiles, how much will Jada pay?

    • 90 \times 5^2 + 58 \times 5^2 \times 0.70
    • 90 \times 25 + 58 \times 25 \times 0.70
    • 2250 + 1450 \times 0.70
    • 2250 + 1015
    • 3265