Exponents and Powers

Exponents and Powers - Sub Topics

  • Exponents and Powers
  • Laws of Exponents
  • Standard Form of a Number
  • Solved Questions on Exponents and Powers
  • Exponents and Powers

    Exponential notation is a concise way to represent repeated multiplication. It involves two essential components: a base and an exponent.

    Example: 104 = 10 × 10 × 10 × 10 = 10000

    In this expression, the number 10 is the base and 4 serves as the exponent, index or power.

    The base indicates the number that needs to be multiplied and the exponent, index or power signifies how many times the base is to be multiplied.

    Note: When a negative number is raised to an even power, the result is always positive.

    Example: (−7)2 = (−7) × (−7) = 49

    When a negative number is raised to an odd power, the outcome is always negative.

    Example: (−7)3 = (−7) × (−7) × (−7) = −343

    Laws of Exponents

    For all non-zero integers 'a' and 'b' and whole numbers 'm' and 'n:


    Note: ⇒  (1)Odd = 1                                           
    ⇒ (1)Even = 1
    ⇒ (−1)Odd = −1                                        
    ⇒ (−1)Even = 1

    Example: Simplify the following expression using laws of exponents:


    a) x4y−1z
    b) x4y−1z3
    c)  x4y−1z6
    d)  x4y−1z9

    Answer: d)  x4y−1z9

    Explanation: Using laws of exponents,


    Standard Form of a Number

    The standard form of a number is a representation where the number is expressed as the product of a decimal number between 1.0 and 10.0 (inclusive of 1.0) multiplied by a power of 10.

    Example: The mass of Mars is 639000000000000000000000 kg. How is the mass of Mars expressed in standard form?        

    a) 6.39 × 1019 kg
    b) 6.39 × 1021 kg
    c) 6.39 × 1022 kg
    d) 6.39 × 1023 kg

    Answer: d) 6.39 × 1023 kg

    Explanation: cmo-exponents-c7-4

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