Question

Помогите, пожалуйста, вычислить, желательно подробно,чтобы понять!
a)3^7*81
_____
3^10

б)(5x/4)^2

в)-6^3+(-2)^6

Answer 1

a)
$frac{ {3}^{7} times 81 }{ {3}^{10} } = frac{ {3}^{7} times {3}^{4} }{ {3}^{10} } = frac{ {3}^{7 + 4} }{ {3}^{10} } = frac{ {3}^{11} }{ {3}^{10} } = {3}^{11 - 10} = {3}^{1} = 3$
б)
$( frac{5x}{4} ) ^{2} = frac{(5x) ^{2} }{ {4}^{2} } = frac{ {5}^{2} times {x}^{2} }{ 16 } = frac{25}{16} {x}^{2} = 1 frac{9}{16} {x}^{2}$
в)
$- {6}^{3} + ( - 2) ^{6} = - (3 times 2) ^{3} + ( - 2) ^{3} times ( - {2})^{3} = - {3}^{3} times {2}^{3} + ( - 8) times ( - 8) = - 27 times 8 + 64 = 8 times ( - 27 + 8) = 8 times ( - 19) = - 152$