Question

${ (\frac{1}{4} )}^{ - 2} - 3 {(8)}^{ \frac{2}{3} } \times {4}^{0} + { \frac{9}{16} }^{ - \frac{1}{2} }$
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Answer 1

Answer:

4.33

Step-by-step explanation:

$\frac{ 1}{4} {}^{ - 2} - 3( {8}^{ \frac{2}{3} } ) \times {4}^{0} + \frac{9}{16} {}^{ - \frac{1}{2} } \\ = {4}^{2} - 3( {2}^{3} ) {}^{ \frac{2}{3} } \times 1 + ( \frac{ {3}^{2} }{ {4}^{2} } ) {}^{ \frac{ - 1}{2} } \\ = 16 - 3(4) + \frac{3 {}^{ - 1} }{4 {}^{ - 1} } \\ = 16 - 12 + 0.33 \\ = 4 + 0.33 \\ = 4.33$

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\textsf{Given that,}$

$\sf{ \bigg(\frac { 1} { 4 } \bigg ) ^ { - 2 } - 3 ( 8 ) ^ \frac { 2 }{3} \times ( {4})^{0} + \bigg( \frac {9} { 16 } \bigg ) ^{ - \frac{1}{2} } }$

$\sf{ = \bigg(\frac { 4 } { 1 } \bigg ) ^ { 2 } - 3 ( {2}^{3} ) ^ \frac { 2 }{3} \times ( 1 ) + \bigg( \frac { 16} { 9 } \bigg ) ^{ \frac{1}{2} } }$

$\sf{ = 16 - 3 \times {2}^{ \cancel3 \times \frac { 2 }{ \cancel3}} + \left \{\bigg( \frac { 4} {3} \bigg ) ^{ 2} \right \} ^{ \frac{1}{2} } }$

$\sf{ = 16 - 3 \times {2}^{2} + \bigg( \frac { 4} {3} \bigg ) ^{ \cancel2 \times \frac{1}{ \cancel2} } }$

$\sf{ = 16 - 3 \times 4 + \frac { 4} {3} }$

$\sf{ = 16 - 12+ \frac { 4} {3} }$

$\sf{ = 4+ \frac { 4} {3} }$

$\sf{ = \frac { 16} {3} }$

$\sf{ =5 \frac { 1} {3} } \: \bf{Ans}.$