Answer
$$\frac{1^7}{\sqrt{3}^7}=\frac{\sqrt{3}}{81}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1^7}{\sqrt{3}^7}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{27\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{27\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{3}}{81}\end{aligned} $$ | |
| 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. $$ \color{blue}{ 1 } \cdot \sqrt{3} = \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 27 \sqrt{3} } \cdot \sqrt{3} = 81 $$ |
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