Question

[(- 2/3)^6 : (-2/3)^4 + (-3/8)^5 :(-3/8)^3]: 1/18
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Answer 1

   
[tex]\displaystyle \\ \left[ \left(- \frac{2}{3} \right)^6 : \left( -\frac{2}{3} \right)^4 + \left( -\frac{3}{8} \right)^5 : \left(- \frac{3}{8} \right)^3 \right] : \frac{1}{18} = \\ \\ = \left[ \left(- \frac{2}{3} \right)^{6-4} + \left( -\frac{3}{8} \right)^{5-3} \right] : \frac{1}{18} = \\ \\ = \left[ \left(- \frac{2}{3} \right)^2 + \left( -\frac{3}{8} \right)^2 \right] : \frac{1}{18} = \\\\ = \left[ \left(\frac{2}{3} \right)^2 + \left( \frac{3}{8} \right)^2 \right] : \frac{1}{18}=[/tex]


[tex]\displaystyle = \left[ \frac{4}{9} + \frac{9}{64} \right] : \frac{1}{18}= \\ \\ \\ = \frac{4\times 64 +9 \times 9}{9 \times 64}: \frac{1}{18} = \\ \\ \\ = \frac{256 +81}{9 \times 64} \times \frac{18}{1} = \\ \\ \\ = \frac{337}{9 \times 64} \times \frac{18}{1} = \\ \\ \\ = \frac{337 \times 18}{9 \times 64} = \frac{337 \times 2}{64} = \boxed{\frac{337}{32}} [/tex]