Question

find values of M and n if 4^2m = cube root of (16)^-6/n =( Square root of 8) ^2

Answer 1

Solution:-

given by:-

${4}^{2m} = \sqrt[3]{ {(16)}^{ - \frac{6}{n} } } = { (\sqrt{8} )}^{2} \\ \\ {2}^{4m} = {2}^{3} \\ 4m = 3 \\ (m = \frac{3}{4} ) \: ans \\ \\ \sqrt[3]{( {16)}^{ - \frac{6}{n} } } = {( \sqrt{8}) }^{2} \\ {16}^{ \frac{ - 6}{n} \times \frac{1}{3} } = {2}^{3} \\ {( {2}^{4} )}^{ \frac{ - 2}{n} } = {2}^{3} \\ {2}^{ - \frac{8}{n} } = {2}^{3} \\ \frac{ - 8}{n } = 3 \\ \frac{ - n}{8} = \frac{1}{3} \\ (n = - \frac{8}{3} ) \: ans \\ i \: hope \: its \: helpfull$