Penjelasan dengan langkah-langkah:
[tex]1. \: \frac{ ({ - 16})^{ - 2}.(16 - {16}^{0}) }{5. {2}^{ - 6} } \\ = \frac{ \frac{1}{( { - 16})^{2} }.(16 - 1) }{5. \frac{1}{ {2}^{6} } } \\ = \frac{ \frac{1}{256} .15}{5. \frac{1}{64} } \\ = \frac{3}{256} \div \frac{1}{64} \\ = \frac{3}{256} \times 64 \\ = \frac{3}{4} [/tex]
[tex]2. \: {3}^{2 {x}^{2} + 5x - 3 } = 1 \\ {3}^{2 {x}^{2} + 5x - 3 } = {3}^{0} \\ 2 {x}^{2} + 5x - 3 = 0 \\ (2x - 1)(x + 3) = 0 \\ 2x - 1 = 0 \: atau \: x + 3 = 0 \\ 2x = 1 \: atau \: x = - 3 \\ x = \frac{1}{2} \: atau \: x = - 3 [/tex]
[tex]3. \: \frac{ {2}^{ \frac{1}{2}}. {3}^{ \frac{1}{2} }. {4}^{ \frac{1}{4} } }{ {10}^{ - \frac{1}{5} } . {5}^{ \frac{3}{5} } } \div \frac{ {3}^{ \frac{4}{3} } . {5}^{ - \frac{7}{5} } }{ {4}^{ - \frac{3}{5} }.6 } \\ = \frac{ {2}^{ \frac{1}{2} }. {3}^{ \frac{1}{2} }. {( {2}^{2}) }^{ \frac{1}{4} } }{ {(2 \times 5)}^{ - \frac{1}{5} } . {5}^{ \frac{3}{5} } } \div \frac{ {3}^{ \frac{4}{3} } . {5}^{ - \frac{7}{5} } }{ {( {2}^{2}) }^{ - \frac{3}{5} }.2.3 } \\ = \frac{ {2}^{ \frac{1}{2} }. {3}^{ \frac{1}{2} }. {2}^{ \frac{1}{2} } }{ {2}^{ - \frac{1}{5} } . {5}^{ - \frac{1}{5} }. {5}^{ \frac{3}{5} } } \times \frac{ {2}^{ - \frac{6}{5} }.2.3 }{ {3}^{ \frac{4}{3} }. {5}^{ - \frac{7}{5} } } \\ = {2}^{ \frac{1}{2} + \frac{1}{2} + ( - \frac{6}{5} ) - ( - \frac{1}{5} ) + 1} . {3}^{ \frac{1}{2} + 1 - \frac{4}{3}}. \frac{1}{ {5}^{ - \frac{1}{5} } + \frac{3}{5} + ( - \frac{7}{5} ) } \\ = {2}^{1 - 1 + 1} . {3}^{ \frac{3}{2} - \frac{4}{3} }. \frac{1}{ {5}^{ - 1} } \\ = 2. {3}^{ \frac{9}{6} - \frac{8}{6} }.5 \\ = 2. {3}^{ \frac{1}{6} } .5 [/tex]
[tex]4. \: \frac{ {x}^{ - 1} + {y}^{ - 2} }{ {x}^{ - 2} + {y}^{ - 1} } \\ = {x}^{ - 1 - ( - 2)} {y}^{ - 2 - ( - 1)} \\ = x {y}^{ - 1} \\ = \frac{x}{y} [/tex]
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