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Common mistakes made when solving the Exponent and Power problems

Though the students enjoy solving the exponents and power problems, however in many cases they tend to make mistakes. These mistakes could be out of carelessness or because the child did not under the concept properly. It is always a good idea to be aware about the common mistakes which students make so that it can be corrected from the early age. Here are some of the common mistakes which students usually make when solving the exponents and power problems.

☞ am+an=am+n

We will try to understand this by an example.

23+24≠27 In this case LHS is not same as RHS.

Ways to teach the children to minimize this error
  • Resolving the above example
    23 means multiplying 2 by itself 3 times (2×2×2)
    24 means multiplying 2 by itself 4 times (2×2×2×2)
    27 means multiplying 2 by itself 7 times (2×2×2×2×2×2×2).
    So the LHS is (2×2×2)+(2×2×2×2) and RHS is (2×2×2)×(2×2×2×2). LHS is NOT same as RHS.
  • Instead from the above we see that 23×24=27. Thus in the similar manner it can be concluded that am×an=am+n

    • ☞ am−an=am−n

    We will try to understand this by an example.

    34−32≠32 In this case LHS is not same as RHS.

    Ways to teach the children to minimize this error
  • Resolving the above example
    34 means multiplying 3 by itself 4 times (3×3×3×3)
    32 means multiplying 3 by itself 2 times (3×3)
    32 means multiplying 3 by itself 2 times (3×3)
    So the LHS is (3×3×3×3)−(3×3) and RHS is (3×3). LHS is NOT same as RHS.
  • Instead from the above we see that 34÷32=32. Thus in the similar manner it can be concluded that am÷an=am−n

    • ☞ am×an=am×n

    We will try to understand this by an example.

    53×52≠56 In this case LHS is not same as RHS.

    Ways to teach the children to minimize this error
  • Resolving the above example
    53 means multiplying 5 by itself 3 times (5×5×5)
    52 means multiplying 5 by itself 2 times (5×5)
    56 means multiplying 5 by itself 6 times (5×5×5×5×5×5)
    So the LHS is (5×5×5)×(5×5) and RHS is (5×5×5×5×5×5). LHS is NOT same as RHS.
  • Instead from the above we see that 53×52=55. Thus in the similar manner it can be concluded that am×an=am+n

    • ☞ am÷an=am÷n

    We will try to understand this by an example.

    106÷103≠102 In this case LHS is not same as RHS.

    Ways to teach the children to minimize this error
  • Resolving the above example
    106 means multiplying 10 by itself 6 times (10×10×10×10×10×10)
    103 means multiplying 10 by itself 3 times (10×10×10)
    102 means multiplying 10 by itself 2 times (10×10)
    So the LHS is (10×10×10×10×10×10)÷(10×10×10) and RHS is (10×10). LHS is NOT same as RHS.
  • Instead from the above we see that 106÷103=103. Thus in the similar manner it can be concluded that am÷an=am−n

    • ☞ na+nb=nc ⇒ a+b=c

    na+nb=nc ⇏ a+b=c

    Ways to teach the children to minimize this error
  • Resolving the above with an example
    24+24=25 (this is true)
    But, 4+4=5 is not true
    ∴ above condition is not correct
  • In fact, na×nb=nc ⇒ a+b=c

    • ☞ na−nb=nc ⇒ a−b=c

    na−nb=nc ⇏ a−b=c

    Ways to teach the children to minimize this error
  • Resolving the above with an example
    24−23=23 (this is true)
    But, 4−3=3 is not true
    ∴ above condition is not correct
  • In fact, na÷nb=nc ⇒ a−b=c

    • ☞ na×nb=nc ⇒ a×b=c

    na×nb=nc ⇏ a×b=c

    Ways to teach the children to minimize this error
  • Resolving the above with an example
    25×26=211 (this is true)
    But, 5×6=11 is not true
    ∴ above condition is not correct
  • In fact, na×nb=nc ⇒ a+b=c

    • ☞ na÷nb=nc ⇒ a÷b=c

    na÷nb=nc ⇏ a÷b=c

    Ways to teach the children to minimize this error
  • Resolving the above with an example
    35÷33=32 (this is true)
    But, 5÷3=2 is not true
    ∴ above condition is not correct
  • In fact, na÷nb=nc ⇒ a−b=c

    • ☞ a0=0

    a0=1 (≠0)

    Ways to teach the children to minimize this error
  • any number to the power of 0 is equal to 1

    • ☞ a1=1

    a1=a (≠1)

    Ways to teach the children to minimize this error
  • any number to the power of 1 is equal to that number

    • ☞ −5²=25

    −5²=−25 (≠25)

    Ways to teach the children to minimize this error
  • Resolving the above
    −5²
    = (−1)×5²
    = (−1)×25
    = −25

    • ☞ 4−3=(−4)(−4)(−4)

    4−3=1/(4×4×4) [≠ (−4)(−4)(−4)]

    Ways to teach the children to minimize this error
  • Resolving the above
    4−3
    = 1/4³
    = 1/(4×4×4)


    • The best way to remove the above confusion and to ensure the children have less chance of committing mistakes is to practice the problems related to the above situations. Click on Exponents & Power to practice.



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    Given below are other commonly made mistakes in Math:
    Clock Reading Time | Exponents & Power | Whole to number-word | Square root | Lines & Angles | Integers | Area Plane Figure | Perimeter Plane Figure | Algebraic Identities | Congruence of Triangles | Similar Triangles | Coordinate Geometry | Trigonometry | Solving equations | Polynomial | Division | Algebraic Expression | Average |
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