Fractional Exponents Practice Question

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first law of exponents
Question 1
Simplify the following:

Answer

Select and check your answer...
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A. 3
B. 1/9
C. 1/3
D. 9
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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.
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