Negative Exponents Questions with Detailed Solutions for Grade 8

Detailed solutions and explanations to Grade 8 questions on simplifying expressions with negative exponents .

Review: Rules of Exponents
Rule 1: (a × b)n = an × bn
Rule 2: (a / b)n = an / bn
Rule 3: a -n = 1 / a n
Rule 4: (a / b) -n = (b / a) n

  1. Simplify the expression 5 -2
    Solution
    Use rule 3 above to write
    5 -2 = 1 / 5 2 = 1 / 25

  2. (-1/3) -2 =
    Solution
    Rewrite expression as follows
    (-1/3) -2 = [ (-1)(1/3) ] -2
    Use rule 1 of exponents
    = (-1) -2 (1/3) -2
    Use rules 3 and 4 of negative exponents
    = [ 1 / (-1) 2 ] [ (3/1) 2 ]
    = [ 1/1 ] [ 9/1 ] = 9

  3. Simplify the expression (5 -1) / (3 -1)
    Solution
    Use rule 2 to rewrite expression as follows
    (5 -1) / (3 -1) = (5 / 3) -1
    Use rule 4 to rewrite expression as follows
    = (3 / 5) 1 = 3 / 5

  4. (2 -3) × (3 -2) =
    Solution
    Use rule 3 to rewrite expression as follows
    (2 -3) × (3 -2) = (1 / 2 3) × (1 / 3 2) = (1 / 8)(1 / 9) = 1 / 72

  5. Simplify the expression - 2 -3
    Solution
    We first rewrite the given expression as follows
    - 2 -3 = (-1)(2 -3)
    We now use rule 3
    = (-1)(1 / 2 3) = (-1)(1 / 8) = - 1 / 8

  6. - 1 -3 + 2 -3 =
    Solution
    Use rule 3 to rewrite the given expression as follows
    - 1 -3 + 2 -3 = (-1) (1 / 1 3) + 1 / 2 3 = - 1 / 1 + 1 / 8 = - 1 + 1 / 8
    Set fractions to common denominator
    = - 8 / 8 + 1 / 8 = - 7 / 8

  7. (- 1) -4 + 2 -3 =
    Solution
    Use rule 3 to rewrite the given expression as follows
    (- 1) -4 + 2 -3 = 1 / (-1) 4 + 1 / 2 3 = 1 / 1 + 1 / 8
    Set fratcions to common denominator
    = 8 / 8 + 1 / 8 = 9 / 8

  8. Simplify the expression (- 4 -2)(2 2)
    Solution
    Use rule 3 to rewrite the given expression as follows
    (- 4 -2)(2 2) = - (1 / 4 2 )(2 2)
    Simplify
    = - (1 / 16)(4) = - 1 / 4

  9. (- 1) -3 + 2 0 =
    Solution
    Note that 2 0 = 1. Use rule 3 to write
    (- 1) -3 + 2 0 = 1 / (- 1) 3 + 1
    Simplify
    = 1 / (-1) + 1 = -1 + 1 = 0

  10. 0 -3 =
    Solution
    Use rule 3 to write
    0 -3 = 1 / 0 3 = 1 / 0 : division by 0 not allowed and therefore 0 -3 is not a real number.

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