$$ (\frac{1}{3})^2 = \frac{ 1 }{ 3 }^{ 2 } \cdot 1 ^ { 2 } = \frac{ 1 }{ 3 }^{ 2 } 1 ^2 = \frac{ 1 }{ 3 }^{ 2 } \lvert 1 \rvert = \frac{1}{9} $$

Combine like terms

Combine like terms

$$ (\frac{1}{3})^2 = \frac{ 1 }{ 3 }^{ 2 } \cdot 1 ^ { 2 } = \frac{ 1 }{ 3 }^{ 2 } 1 ^2 = \frac{ 1 }{ 3 }^{ 2 } \lvert 1 \rvert = \frac{1}{9} $$

Add $ \dfrac{-7}{9} $ and $ \dfrac{1}{9} $ to get $ \dfrac{-6}{9} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{-7}{9} + \frac{1}{9} & = \frac{-7}{\color{blue}{9}} + \frac{1}{\color{blue}{9}} =\frac{ -7 + 1 }{ \color{blue}{ 9 }} = \\[1ex] &= \frac{-6}{9} \end{aligned} $$

Subtract $4$ from $ \dfrac{-6}{9} $ to get $ \dfrac{ \color{purple}{ -42 } }{ 9 }$.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{9}$.

$$ \begin{aligned} \frac{-6}{9} -4 & \xlongequal{\text{Step 1}} \frac{-6}{9} - \frac{4}{\color{red}{1}} = \frac{ -6 }{ 9 } - \frac{ 4 \cdot \color{blue}{ 9 }}{ 1 \cdot \color{blue}{ 9 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -6 } }{ 9 } - \frac{ \color{purple}{ 36 } }{ 9 }=\frac{ \color{purple}{ -42 } }{ 9 } \end{aligned} $$