Question

Simplify:
(7 to the power 5/6 into 7 to the power 2/3) (2 to the power 5/8 into 3 to the power 5/8)

Answer 1

Hey here is your answer
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$= { { (\frac{5}{7}) }^{7} \times {( \frac{2}{3}) }^{7} } \: \times {( \frac{5}{8} )}^{2} \times {( \frac{5}{8} )}^{3} \\ \\ = {5}^{7} \times {7}^{ - 7} \times {2}^{7} \times {3}^{ - 7} \times { (\frac{5}{8}) }^{2 + 3} \\ \\ = {5}^{7} \times {7}^{ - 7} \times {2}^{7} \times {3}^{ - 7} \times {5}^{5} \times { {2}^{3} }^{ - 5} \\ \\ = {5}^{7 + 5} \times {7}^{ - 7} \times {2}^{7 - 15} \times {3}^{ - 7 } \\ \\ = \frac{ {5}^{12} }{ {7}^{ 8} } \times \frac{ {2}^{22} }{ {3}^{8} }$
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Hope it may helpful to you