Question

обчисліть значення виразу
$16 {}^{ - 0.75} \times 8 {}^{ - \frac{5}{12} } \times 4 {}^{ \frac{5}{8} }$
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Answer 1

${16}^{ - 0.75} \times {8}^{ - \frac{5}{12} } \times {4}^{ \frac{5}{8} } = (2 {}^{4} ) {}^{ - \frac{3}{4} } \times( {2}^{3} ) {}^{ - \frac{5}{12} } \times ({2}^{2} ) {}^{ \frac{5}{8} } = \\ = 2 {}^{4 \times ( - \frac{3}{4}) } \times 2 {}^{3 \times ( - \frac{5}{12}) } \times 2 {}^{2 \times \frac{5}{8} } = {2}^{ - 3} \times 2 {}^{ - \frac{5}{4} } \times 2 {}^{ \frac{5}{4} } = \\ = {2}^{ - 3 - \frac{5}{4} + \frac{5}{4} } = {2}^{ - 3} = \frac{1}{2 {}^{3} } = \frac{1}{8} = 0.125$