Question

(root 2 /root 3)^5 × (6/7)^2

Answer 1

Mark this answer as brainliest answer

Answer 2

$Given \: \Big(\frac{\sqrt{2}}{\sqrt{3}}\Big)^{5} \times \Big(\frac{6}{7}\Big)^{2}$

$= \frac{ \sqrt{2} \times \sqrt{2} \times\sqrt{2} \times\sqrt{2} \times \sqrt{2} }{ \sqrt{2} \times \sqrt{3} \times\sqrt{3} \times\sqrt{3} \times \sqrt{3} } \times \frac{36}{49}$

$= \frac{2\times 2 \times \sqrt{2}}{3\times 3 \times \sqrt{3}} \times \frac{36}{49} \\= \frac{4\sqrt{2}}{9\sqrt{3}} \times \frac{36}{49}$

/* After cancellation,we get */

$= \frac{16\sqrt{2}}{49\sqrt{3}}$

Therefore.,

$\red {\Big(\frac{\sqrt{2}}{\sqrt{3}}\Big)^{5} \times \Big(\frac{6}{7}\Big)^{2}} \green {= \frac{16\sqrt{2}}{49\sqrt{3}}}$

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