Fractional Exponents Practice Question

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Question 1

Simplify the following:

first law of exponents


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Select and check your answer...

A. 3
B. 1/9
C. 1/3
D. 9

Step by Step Solution

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    Step 1

    Notice the negative exponent? Now, it is better to change it into positive exponent using the exponent law as shown on the right.

    This term now becomes:

    27 to the power of negative 2 over 3
    Changing negative exponent to positive exponent
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    Step 2

    Now, let's apply the fractional exponent formula that we have just learned earlier on.

    Hence, this term becomes:

    Changing the term into roots symbol
    Formula relating fractional exponents with roots
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    Step 3

    Next, cube root of 27 is 3. (i.e. 27 = 3 x 3 x 3)

    Hence, this term becomes:

    Simplifying the term to get 1 over 3 to the power of 2
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    Step 4

    Now, (3)2 = 3 x 3 = 9. Therefore, we get:

    The answer is 1/9

    Clearly, the answer is B.