№7 Упростите выражение a) $$\frac{a^8 \times a^6}{a^{10}}$$ б) $$\frac{(a^4)^3 \times a^2}{a^{11}}$$ в) $$(\frac{(a^6 \times b^3)^7}{a^{40}})^5$$

a) $$\frac{a^8 \times a^6}{a^{10}} = \frac{a^{8+6}}{a^{10}} = \frac{a^{14}}{a^{10}} = a^{14-10} = a^4$$ б) $$\frac{(a^4)^3 \times a^2}{a^{11}} = \frac{a^{4\times 3} \times a^2}{a^{11}} = \frac{a^{12} \times a^2}{a^{11}} = \frac{a^{12+2}}{a^{11}} = \frac{a^{14}}{a^{11}} = a^{14-11} = a^3$$ в) $$(\frac{(a^6 \times b^3)^7}{a^{40}})^5 = (\frac{a^{6\times 7} \times b^{3\times 7}}{a^{40}})^5 = (\frac{a^{42} \times b^{21}}{a^{40}})^5 = (a^{42-40} \times b^{21})^5 = (a^2 \times b^{21})^5 = a^{2\times 5} \times b^{21 \times 5} = a^{10}b^{105}$$