Question

What's the reciprocal of 2⁵ * 3⁷ * (√7)raised to power of ¾ upon (√8)² * √7 ?​

Answer 1

Answer:

$\frac{ {7}^{ \frac{1}{8} } }{ {2}^{ \frac{3}{4} } \times {3}^{ \frac{21}{4} } }$

Step-by-step explanation:

$\frac{ ( {{2}^{5} \times {3}^{7} \times \sqrt{7}})^{ \frac{3}{4} } }{ { \sqrt{8} }^{2} \times \sqrt{7} } = \frac{ {2}^{ \frac{15}{4} } \times {3}^{ \times \frac{21}{4} } \times {7}^{ \frac{3}{8} } }{8 \times \sqrt{7} } \\ reciprocal \: of \: the \: above\: equation \: = \frac{ {2}^{3} \times {7}^{ \frac{1}{2} } }{2 \frac{15}{4} \times {3}^{ \frac{21}{4} } \times {7}^{ \frac{3}{8} } } \\ = {2}^{ - \frac{3}{4} } \times {3}^{ - \frac{21}{4} } \times {7}^{ \frac{1}{8} } \\ = \frac{ {7}^{ \frac{1}{8} } }{ {2}^{ \frac{3}{4} } \times {3}^{ \frac{21}{4} } }$