179k views
5 votes
" Use the rational exponent property to rewrite 27 2/3 as an integer. Enter your numeric answer. 3 9 81 19683

1 Answer

5 votes

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.

Learn more about Rational Exponent Property

User Bryan Rowe
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories