Evaluate. ((2)/(3))^(3)+(2)/(9) Write your answer in simplest form.

Evaluate first term: Evaluate the first term ((2/3)^(3)). To evaluate ((2/3)^(3)), we need to cube both the numerator and the denominator. (2^3)/(3^3) = 8/27Add second term: Add the second term (2/9) to the result from Step 1. We have 8/27 from the first term, and we need to add this to 2/9. To add fractions, they must have a common denominator. The common denominator for 27 and 9 is 27.Convert second term: Convert the second term (2/9) to have the common denominator of 27. To convert 2/9 to a denominator of 27, we multiply both the numerator and the denominator by 3. (2/9) * (3/3) = (2*3)/(9*3) = 6/27Add fractions: Add the two fractions with the common denominator. Now we add 8/27 and 6/27. 8/27 + 6/27 = (8+6)/27 = 14/27Check for simplification: Check if the result can be simplified further. The fraction 14/27 cannot be simplified further because 14 and 27 have no common factors other than 1.

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Evaluate. $\left(\frac{2}{3}\right)^3+\frac{2}{9}$ Write your answer in simplest form.

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Algebra 2

Evaluate rational exponents

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Q. Evaluate.

\left(\frac{2}{3}\right)^3+\frac{2}{9}

Write your answer in simplest form.

Evaluate first term: Evaluate the first term $\left(\frac{2}{3}\right)^{3}$ . To evaluate $\left(\frac{2}{3}\right)^{3}$ , we need to cube both the numerator and the denominator. $\frac{2^3}{3^3} = \frac{8}{27}$
Add second term: Add the second term $\frac{2}{9}$ to the result from Step $1$ . $\newline$ We have $\frac{8}{27}$ from the first term, and we need to add this to $\frac{2}{9}$ . $\newline$ To add fractions, they must have a common denominator. The common denominator for $27$ and $9$ is $27$ .
Convert second term: Convert the second term $(\frac{2}{9})$ to have the common denominator of $27$ . $\newline$ To convert $\frac{2}{9}$ to a denominator of $27$ , we multiply both the numerator and the denominator by $3$ . $\newline$ $(\frac{2}{9}) \times (\frac{3}{3}) = (\frac{2\times3}{9\times3}) = \frac{6}{27}$
Add fractions: Add the two fractions with the common denominator. $\newline$ Now we add $\frac{8}{27}$ and $\frac{6}{27}$ . $\newline$ $\frac{8}{27} + \frac{6}{27} = \frac{(8+6)}{27} = \frac{14}{27}$
Check for simplification: Check if the result can be simplified further. $\newline$ The fraction $\frac{14}{27}$ cannot be simplified further because $14$ and $27$ have no common factors other than $1$ .