Question

The value of ( 8^-4/3 * 2^-2) ^1/2

Answer 1

Answer:2730 2/3

Step-by-step explanation:

Answer 2

$\: \: \: \: {( {8}^{ \frac{ - 4}{3} } \times {2}^{ - 2}) }^{ \frac{1}{2} } \\ = ({8}^{ \frac{ - 4}{3} \times \frac{1}{2} }) \times ( {2}^{ (- 2) \times \frac{1}{2} } ) \\ = ( {8}^{ \frac{ - 2}{3} } ) \times ( {2}^{ - 1} ) \\ = ( \frac{1}{ {8}^{ \frac{2}{3} } }) \times ( \frac{1}{ {2}^{1} } ) \\ = ( \frac{1}{ {( {8}^{2} )}^{ \frac{1}{3} } } ) \times ( \frac{1}{2} ) \\ = \frac{1}{ {64}^{ \frac{1}{3} } } \times \frac{1}{2} \\ = \frac{1}{ {( {4}^{3} )}^{ \frac{1}{3} } } \times \frac{1}{2} \\ = \frac{1}{ {4}^{1} } \times \frac{1}{2} \\ = \frac{1}{4} \times \frac{1}{2} \\ = \frac{1}{8}$