Exponent Laws Questions

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Question 2

Simplify the following expression:

Expression to simplify

The following pictures are the exponent laws. You can use them as reference.

  • first law of exponents
  • second law of exponents
  • third law of exponents
  • fourth law of exponents
  • fifth law of exponents
  • law of exponents

Answer

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Select and check your answer...

A. 3s
B. 3qs
C. 3q
D. 3q2s

Step by Step Solution

  • Lesson Icon

    Step 1

    Let's first focus on the numerator:

    6(q2s3)2

    Using the exponent law* as shown in the picture, we get:

    6(q2s3)2 = 6q2 x 2 s3 x 2

    *Note: If you are not sure on how to derive this law, you can see it at step 3 in this practice question.

    Previously derived law of exponents
    Applying the derived exponent law
  • Lesson Icon

    Step 2

    Now,

    2 multiply by 2 gives 4, and
    3 multiply by 2 gives 6.

    Hence, we have 6q4s6.

    Simplying the expression to get 4 p^4 s^6
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    Step 3

    Next, let's focus on the denominator:

    2(qs2)3

    Using the exponent law* as shown in the picture, we get:

    2(qs2)3 = 2q1 x 3 s2 x 3

    *Note: If you are not sure on how to derive this law, you can see it at step 3 in this practice question.

    Previously derived law of exponents
    Applying the derived exponent law
  • Lesson Icon

    Step 4

    Now,

    1 multiply by 3 gives 3, and
    2 multiply by 3 gives 6.

    Hence, we have 2q3s6.

    Simplying to get 2q^3 s^6
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    Step 5

    Now, after simplifying the numerator and denominator, the original expression becomes:

    6q4s6 ÷ 2q3s6
    The expression after simplifying the numerator and denominator
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    Step 6

    Using the exponent law as shown in the picture, we get:

    6q4s6 ÷ 2q3s6
    = 3q4 - 3 s6 - 6
    second law of exponents
    The expression after applying the second law of exponents
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    Step 7

    Simplifying,

    3q4 - 3 s6 - 6

    We get:

    3q1 s0

    Now, we can write:

    q1 as q and,
    s0 as 1
    q^1 equals to q and s^0 equals 1
  • Lesson Icon

    Step 8

    Finally, we have the simplest term, 3q

    Clearly, the answer is C.

    The final expression is 3q