Question

очень нужно прям очеен номер 10.12

Answer 1

10.12. Упростите:

$1) \frac{a {}^{ - \frac{1}{2} } \sqrt{a {}^{3} } }{a {}^{ - \frac{1}{4} } \times a {}^{ \frac{7}{6} } } = \frac{a {}^{ - \frac{1}{2} } \times a^ \frac{3}{2} }{a {}^{ - \frac{1}{12} } } = a {}^{ - \frac{1}{2} } \times a {}^{ \frac{19}{12} } = a {}^{ \frac{13}{12} } = \sqrt[12]{a {}^{13} } = a \sqrt[12]{a}$

$2) \frac{x {}^{ \frac{1}{3} } \times \sqrt[3]{x} }{ x{}^{ - \frac{4}{3} } } = \frac{x {}^{ \frac{1}{3} } \times x {}^{ \frac{1}{3} } }{x {}^{ - \frac{4}{3} } } = \frac{x ^\frac{2}{3} }{x {}^{ - \frac{4}{3} } } = x {}^{2}$

$3) \frac{a - 16a {}^{0.5} }{5a {}^{0.25} + 20} = \frac{a - 16a {}^{ \frac{1}{2} } }{5a {}^{ \frac{1}{4} } + 20 } = \frac{a {}^{ \frac{1}{2} } \times (a {}^{ \frac{1}{2} } - 16)}{5(a {}^{ \frac{1}{4} } + 4) } = \frac{a {}^{ \frac{1}{2} } \times (a {}^{ \frac{1}{4} } - 4) \times (a {}^{ \frac{1}{4} } + 4) }{5(a {}^{ \frac{1}{4} } + 4) } = \frac{{a {}^{ \frac{1}{2} } \times }^{} (a {}^{ \frac{1}{4} } - 4) }{5} = \frac{a {}^{ \frac{3}{4} } - 4a {}^{ \frac{1}{2} } }{5} = \frac{ \sqrt[4]{a {}^{3} } - 4 \sqrt{a} }{5}$