Question

8^-2/3*4^-3/2*2^3/16^2 find value

Answer 1

Heya !!!

Identities used :

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ {a}^{m} \times {a}^{n} = {a}^{m + n}$


${8}^{ - \frac{2}{3} } \times {4}^{ - \frac{3}{2} } \times \frac{ {2}^{3} }{ {16}^{2} } \\ \\ = {(2}^{3} )^{ - \frac{2}{3} } \times {(2}^{2} )^{ - \frac{3}{2} } \times \frac{ {2}^{3} }{ {( {2}^{4} )}^{2} } \\ \\ = {2}^{3 \times - \frac{2}{3} } \times {2}^{2 \times - \frac{3}{2} } \times \frac{ {2}^{3} }{ {2}^{8} } \\ \\ = {2}^{ - 2} \times {2}^{ - 3} \times {2}^{3 - 8} \\ \\ = {2}^{ - 2} \times {2}^{ - 3} \times {2}^{ - 5} \\ \\ = {2}^{ - 2 + ( - 3) + ( - 5)} \\ \\ = {2}^{ - 2 - 3 - 5} \\ \\ = {2}^{ - 10}$

Hope this helps ☺