Question
Answer
$$3^7-9\cdot3^6+35\cdot3^5-75\cdot3^4+93\cdot3^3-63\cdot3^2+18\cdot3^1=54$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3^7-9\cdot3^6+35\cdot3^5-75\cdot3^4+93\cdot3^3-63\cdot3^2+18\cdot3^1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2187-9\cdot729+35\cdot243-75\cdot81+93\cdot27-63\cdot9+18\cdot3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}2187-6561+8505-6075+2511-567+54 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}54\end{aligned} $$ | |
| ① | A polynomial raised to the power of one equals itself. |
| ② | $$ 9 \cdot 729 = 6561 $$ |
| ③ | $$ 35 \cdot 243 = 8505 $$ |
| ④ | $$ 75 \cdot 81 = 6075 $$ |
| ⑤ | $$ 93 \cdot 27 = 2511 $$ |
| ⑥ | $$ 63 \cdot 9 = 567 $$ |
| ⑦ | $$ 18 \cdot 3 = 54 $$ |
| ⑧ | Combine like terms: $$ \color{blue}{2187} \color{red}{-6561} + \color{green}{8505} \color{orange}{-6075} + \color{blue}{2511} \color{red}{-567} + \color{red}{54} = \color{red}{54} $$ |
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