Question

даю 25 балів!!! завдання 8 та 9

Answer 1

$\displaystyle\bf\\8)\\\\3m^{4} n^{3} =-2\\\\(3m^{4} n^{3} )^{2} =(-2)^{2} \\\\9m^{8} n^{6} =4\\\\9m^{8} n^{6} \cdot 2=4\cdot 2\\\\\boxed{18m^{8} n^{6} =8}\\\\9)\\\\b) \ \ \Big(-1\frac{1}{3} \Big)^{5} \cdot\Big(\frac{3}{4}\Big)^{8} =\Big(-\frac{4}{3} \Big)^{5} \cdot\Big(\frac{3}{4}\Big)^{5} \cdot\Big(\frac{3}{4}\Big)^{3} =\\\\\\=-\Big(\underbrace{\frac{4}{3} \cdot\frac{3}{4}}_{1} \Big)^{5} \cdot\Big(\frac{3}{4}\Big)^{3} =-1\cdot\frac{27}{64} =-\frac{27}{64}$

$\displaystyle\bf\\a) \ \ \frac{3^{7} \cdot 5^{13} }{75^{6} } =\frac{3^{7} \cdot 5^{13} }{(3\cdot 5^{2}) ^{6} } =\frac{3^{7} \cdot 5^{13} }{3^{6} \cdot 5^{12} } =3^{7-6} \cdot 5^{13-12} =3\cdot 5=15$