Final answer:
Using the rational exponent property, 27 raised to the power of 2/3 can be rewritten as ((27) to the power of 1/3) to the power of 2 or (27 to the power of 2) to the power of 1/3. Both these rewrites give us the integer 9.
Step-by-step explanation:
To rewrite 272/3 as an integer using the rational exponent property, we first need to understand what the term 'rational exponent property' means. The rational exponent property tells us that when we have a fraction as an exponent, the numerator represents the power whereas the denominator represents the root. Therefore, 272/3 can be rewritten as (272)1/3 or ((27)1/3)2.
The cube root of 27 is 3. Therefore, when we rewrite 272/3 as ((27)1/3)2, we get 32 which results in 9 as an integer. Conversely, if we rewrite 272/3 as (272)1/3, we get 7291/3, which is also 9. Thus, 9 is our final answer.
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