Question

(3-(1/3)2степень - 1/3):23-(1/9)2степень

Answer 1

(2 2/3)2(степень) - 1/69 - 1/81 = 4 4/9 - 1/69 - 1/81 = 120/3 - 23/3 - 27/3 = 70/3 = 23 1/3

Answer 2

Let's simplify the expression step by step:

1. Calculate the values within the parentheses first:

   • $3 - \frac{1}{3^2} = 3 - \frac{1}{9} = \frac{24}{9} - \frac{1}{9} = \frac{23}{9}$
   • $\frac{1}{9^2} = \frac{1}{81}$

2. Substitute these values back into the expression: $\frac{23}{9} - \frac{1}{81}$

3. Find a common denominator to subtract these fractions: To do this, we'll need to make the second fraction's denominator the same as the first fraction's denominator, which is 9. So, we'll multiply both the numerator and denominator of the second fraction by 9 to get a common denominator.

   $\frac{23}{9} - \frac{1 \cdot 9}{81} = \frac{23}{9} - \frac{9}{81}$

4. Now that we have a common denominator, subtract the fractions: $\frac{23}{9} - \frac{9}{81}$

5. We can simplify further by finding a common factor between 9 and 81, which is 9: $\frac{23}{9} - \frac{1}{9}$

6. Finally, subtract the numerators while keeping the common denominator: $\frac{23 - 1}{9} = \frac{22}{9}$

So, the simplified expression is $\frac{22}{9}$.