Algebra 1b: Unit 1 Obj 3 ~ Simplify Division Of Like Bases

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| By Vicki Barr
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Vicki Barr
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Algebra 1b: Unit 1 Obj 3 ~ Simplify Division Of Like Bases - Quiz

Rules of exponents: subtract exponents when like bases are divided


Questions and Answers
  • 1. 

    When a problem is asking to divide two base numbers that are the same, but with different exponents, what operation do I use for the exponents?

    • A.

      Add

    • B.

      Subtract

    • C.

      Multiply

    • D.

      Divide

    Correct Answer
    B. Subtract
    Explanation
    When dividing two base numbers with different exponents, you subtract the exponents. This is because when dividing, you are essentially canceling out the common factors between the two numbers. Subtracting the exponents ensures that you are dividing the base numbers correctly and obtaining the correct result.

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  • 2. 

    All bases have an exponent

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    When a base has no exponent written it is assumed to be 1, thus all bases have an exponent even if none is written.

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  • 3. 

    Any base raised to this power will equal one

    Correct Answer
    0
    zero
    Explanation
    Any number raised to the power of zero equals one. This is a fundamental rule in mathematics. Therefore, any base raised to the power of zero will also equal one. In this case, the base is zero, so zero raised to the power of zero equals one.

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  • 4. 

    Simplify

    • A.

      4x^3/y

    • B.

      4x/y

    • C.

      X^3y/4

    • D.

      4y/x^3

    Correct Answer
    A. 4x^3/y
    Explanation
    The given expression is 4x^3/y. To simplify this expression, we can divide both the numerator and denominator by 4. This gives us x^3/y. Therefore, the correct answer is x^3/y.

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  • 5. 

    Which one do you like?

    Correct Answer
    C.
  • 6. 

    3a5b2/9a2b5

    • A.

      5ab^8

    • B.

      15a^2

    • C.

      A^3/3b^3

    Correct Answer
    C. A^3/3b^3
    Explanation
    The given expression is a division of two terms. In the numerator, we have a^3, which means a multiplied by itself three times. In the denominator, we have 3b^3, which means 3 multiplied by b multiplied by itself three times. When we divide a^3 by 3b^3, we can simplify the expression by canceling out common factors. We can cancel one 'a' from the numerator with one 'a' from the denominator, leaving us with a^2 in the numerator. Similarly, we can cancel one 'b' from the numerator with one 'b' from the denominator, leaving us with 3b^2 in the denominator. Therefore, the simplified expression is a^2/3b^2.

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  • 7. 

    Write as a single power. 

    Correct Answer
    d^2
    Explanation
    The given expression, d^2, represents d raised to the power of 2. This means that d is multiplied by itself.

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  • 8. 

    Simplify.

    Correct Answer
    3125
  • 9. 

    Write as a single power.

    Correct Answer
    m^9
    Explanation
    The given expression, m^9, represents m raised to the power of 9. This means that m is multiplied by itself 9 times.

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  • 10. 

    Simplify

    • A.

      15a^2

    • B.

      15a^3

    • C.

      15a^3b^0

    • D.

      28a^3b^0

    • E.

      28a^3

    Correct Answer
    B. 15a^3
    Explanation
    The correct answer is 15a^3 because it is the simplest form of the given expressions. The other options have additional terms or factors that can be simplified or removed.

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  • 11. 

    • A.

      A

    • B.

      B

    • C.

      C

    • D.

      D

    • E.

      E

    Correct Answer
    A. A

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