simplify (x^{-12/5}y^{-3/16}2^{4/3})^{5/6}

الحلّ

simplify

(x^{- \frac{12}{5}} \cdot y^{- \frac{3}{16}} \cdot 2^{\frac{4}{3}})^{\frac{5}{6}}

\frac{2 \cdot 2 ^{\frac{1}{9}}}{x ^{2} y ^{\frac{5}{32}}}

خطوات الحلّ

(x^{- \frac{12}{5}} y^{- \frac{3}{16}} \cdot 2^{\frac{4}{3}})^{\frac{5}{6}}

(a \cdot b)^{n} = a^{n} b^{n}

:فعّل قانون القوى

(x^{- \frac{12}{5}} y^{- \frac{3}{16}} \cdot 2^{\frac{4}{3}})^{\frac{5}{6}} = (x^{- \frac{12}{5}})^{\frac{5}{6}} (y^{- \frac{3}{16}})^{\frac{5}{6}} (2^{\frac{4}{3}})^{\frac{5}{6}}

= (x^{- \frac{12}{5}})^{\frac{5}{6}} (y^{- \frac{3}{16}})^{\frac{5}{6}} (2^{\frac{4}{3}})^{\frac{5}{6}}

(x^{- \frac{12}{5}})^{\frac{5}{6}}

بسّط:

\frac{1}{x ^{2}}

= \frac{1}{x ^{2}} (y^{- \frac{3}{16}})^{\frac{5}{6}} (2^{\frac{4}{3}})^{\frac{5}{6}}

(y^{- \frac{3}{16}})^{\frac{5}{6}}

بسّط:

\frac{1}{y ^{\frac{5}{32}}}

= \frac{1}{x ^{2}} \cdot \frac{1}{y ^{\frac{5}{32}}} (2^{\frac{4}{3}})^{\frac{5}{6}}

(2^{\frac{4}{3}})^{\frac{5}{6}} = 2 \cdot 2^{\frac{1}{9}}

= \frac{1}{x ^{2}} \cdot \frac{1}{y ^{\frac{5}{32}}} \cdot 2 \cdot 2^{\frac{1}{9}}

\frac{1}{x ^{2}} \cdot \frac{1}{y ^{\frac{5}{32}}} \cdot 2 \cdot 2^{\frac{1}{9}}

بسّط:

\frac{2 \cdot 2 ^{\frac{1}{9}}}{x ^{2} y ^{\frac{5}{32}}}

= \frac{2 \cdot 2 ^{\frac{1}{9}}}{x ^{2} y ^{\frac{5}{32}}}

7 = \frac{4}{3} (x + 6)

49 x^{2} - 70 x + 25 = 64

x^{3} - 7 x^{2} + 14 x - 8

w^{2} - 16 w + 64