Question
Answer
$$\dfrac{\sqrt{10}^4}{\sqrt{13}^7}=\dfrac{100\sqrt{13}}{28561}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{10}^4}{\sqrt{13}^7}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{100}{2197\sqrt{13}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{100}{2197\sqrt{13}}\frac{\sqrt{13}}{\sqrt{13}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{100\sqrt{13}}{28561}\end{aligned} $$ | |
| ① | $$ \sqrt{10}^4 =
\left( \sqrt{10} ^2 \right)^{ 2 } =
\lvert 10 \rvert ^{ 2 } =
100 $$ |
| ② | $$ \sqrt{13}^7 =
\left( \sqrt{13} ^2 \right)^{ 3 } \cdot \sqrt{13} =
\lvert 13 \rvert ^{ 3 } \cdot \sqrt{13} =
2197\sqrt{13} $$ |
| ③ | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{13}} $$. |
| ④ | Multiply in a numerator. $$ \color{blue}{ 100 } \cdot \sqrt{13} = 100 \sqrt{13} $$ Simplify denominator. $$ \color{blue}{ 2197 \sqrt{13} } \cdot \sqrt{13} = 28561 $$ |
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