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Exponents Worksheet

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Answers and Explanations

 

  1. x • x = x2
    Rewrite x • x with exponents.
    x1x1

    Bases are the same. Keep the base and add the exponents.
    x1x1 = x1+1 = x2

  2. x + x = 2x
     x + x is not the same as x • x. This exercise requires addition of terms, not multiplication.

    Add:
    x + x = 1x + 1x = 2x

  3. a4b4= a4b4
    Because the bases are different (a and b), don't add the exponents.
    a4b4 = a4b4

  4. a-2a6= a4
    Bases are the same. Keep the base and add the exponents.
    a-2a6 = a-2+6 = a4

  5. (xyz)5 • (xyz)15= (xyz)20
    Bases are the same. Keep the base and add the exponents.
    (xyz)5 • (xyz)15 = (xyz)5+15 = (xyz)20

  6. (20e)(20e)= 400e2
    Rewrite (20e)(20e) with exponents.
    (20e1)(20e1)

    Bases are the same. Keep the base and add the exponents. (Remember to multiply 20 and 20.)
    (20e1)(20e1) = 20* 20 * e1 *e1 = 400 *e1+1 = 400e2

  7. (12 + y)30 • (12 + y)8 = (12 + y)38
    Bases are the same. Keep the base and add the exponents.
    (12 + y)30 • (12 + y)8 = (12 + y)30+8 = (12 + y)38

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