Question

15,16,22.

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Answer 1

15.

$y(5y+2x)-(x+y)^2 = 5y^2 + 2xy - x^2 - 2xy - y^2 = 4y^2 - x^2 = 4(\sqrt{3})^2 - (\sqrt{11})^2 = 4*3-11 = 12 - 11 = 1.\\Answer: 1$

16.

$\frac{(c^{-8})^{-6}}{c^{-4}} = \frac{c^{(-8)*(-6)}}{c^{-4}} = \frac{c^{48}}{c^{-4}} = c^{48-(-4)} = c^{48+4} = c^{52}.\\Answer: c^{52}$

22.

$a^{10}(a^{-3})^5 = a^{10}*a^{(-3)*5} = a^{10} * a^{-15} = a^{10+(-15)} = a^{-5} = (\frac{1}{8})^{-5} = 8^5 = (2^3)^5 = 2^{5*3} = 2^{15}\\Answer: 2^{15}$