Question

From Maths Exercise Named :- Indices ⚜⚜

3^-6/7 × 4^-3/7 × 9^3/7 × 2^6/7 / 2^2 + 2^0 + 2^-2
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Question...

Answer Of This Question Is :- 4/21 ...

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Answer 1

$\underline{\sf{\green{Question}}}$

$\sf \dfrac{ {3}^{ \frac{ -6}{ \: 7} } \times {4}^{ \frac{ - 3}{ \: 7} } \times {9}^{ \frac{3}{7} } \times {2}^{ \frac{6}{7} } }{ {2}^{2} + {2}^{0} + {2}^{ - 2} }$

$\underline{\sf{\green{Step~By ~Step Explanation}}}$

$\implies \sf \dfrac{ {3}^{ \frac{ -6}{ \: 7} } \times {4}^{ \frac{ - 3}{ \: 7} } \times {9}^{ \frac{3}{7} } \times {2}^{ \frac{6}{7} } }{ {2}^{2} + {2}^{0} + {2}^{ - 2} } \\\\\implies \sf \dfrac{ {3}^{ \frac{ -6}{ \: 7} } \times { {2} }^{ 2 \times \frac{ - 3}{ \: 7} } \times { {3}}^{2 \times \frac{3}{7} } \times {2}^{ \frac{6}{7} } }{ 4 + 1 + \frac{1}{ {2}^{2} } } \\\\ \implies\sf \dfrac{ {3}^{ \frac{ -6}{ \: 7} } \times { {2} }^{ \frac{ - 6}{ \: 7} } \times { {3}}^{\frac{6}{7} } \times {2}^{ \frac{6}{7} } }{ 5 + \frac{1}{ 4 } } \\\\\implies \sf \dfrac{ {3}^{ \frac{ -6}{ \: 7} } \times { {3}}^{\frac{6}{7} } \times { {2} }^{ \frac{ - 6}{ \: 7} }\times {2}^{ \frac{6}{7} } }{ \frac{20 + 1}{ 4 } } \\\\\implies \sf \dfrac{ {3}^{ \frac{ -6}{ \: 7} + \frac{6}{7} } \times { {2} }^{ \frac{ - 6}{ \: 7} + \frac{6}{7} } }{ \frac{21}{ 4 } } \\\\\implies \sf \dfrac{ {3}^{ \frac{ -6 + 6}{ \: \: \: 7} } \times { {2} }^{ \frac{ - 6 + 6}{ \: \: \: 7} } }{ \frac{21}{ 4 } } \\ \\ \implies\sf \dfrac{ {3}^{ \frac{ 0}{ 7} } \times { {2} }^{ \frac{ 0}{ 7} } }{ \frac{21}{ 4 } } \\\\ \implies\sf \dfrac{ {3}^{0 } \times { {2} }^{ 0}}{ \frac{21}{ 4 } } \\\\\implies \sf \dfrac{ 1 \times 1}{ \frac{21}{ 4 } } \\\\ \implies\sf \dfrac{ 1 }{ \frac{21}{ 4 } } \\\\\implies\underline{\boxed{ \bf \dfrac{ 4}{ 21}}}$

Answer 2

Answer:

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