Answer
$$\frac{4}{7\sqrt{3}^7}=\frac{4\sqrt{3}}{567}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{7\sqrt{3}^7}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4}{7\cdot27\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4}{189\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4}{189\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4\sqrt{3}}{567}\end{aligned} $$ | |
| ① | $$ \sqrt{3}^7 =
\left( \sqrt{3} ^2 \right)^{ 3 } \cdot \sqrt{3} =
\lvert 3 \rvert ^{ 3 } \cdot \sqrt{3} =
27\sqrt{3} $$ |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ 4 } \cdot \sqrt{3} = 4 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 189 \sqrt{3} } \cdot \sqrt{3} = 567 $$ |
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