№4.
б) а⁸(а⁻⁴)³ = а⁸ × а⁻⁴*³ = а⁸ × а ⁻¹² = а ⁸⁺⁽⁻¹²⁾ = а⁻⁴ = 1/a⁴
ж) (n⁴/n⁻⁷)⁻² × n⁻⁵ =(n⁴⁻⁽⁻⁷⁾ )⁻² × n⁻⁵ =(n¹¹)⁻² × n⁻⁵ =
= n ⁻²² × n⁻⁵ = n ⁻²²⁺⁽⁻⁵⁾ = n ⁻²⁷ = 1/n²⁷
и) (3/х³ × х³/6) ⁻¹ = (1/2) ⁻¹ = 2
№5.
б)
(m² - 9)/m ÷ (m-3)² /m + 6/(3-m) =
= (m-3)(m+3) /m × m/(m-3)(m-3) + 6/(3-m) =
= (m+3)/(m-3) + 6/ -(m - 3) =
= (m + 3)/(m -3) - 6/(m-3) =
= (m + 3 - 6)/(m - 3) =
= (m-3) / (m - 3) =
= 1
д)
( (c-d)/d + 2c/(c-d) ) ÷ (c²+d²)/(c-d) =
= ((c-d)(c-d) + 2cd) / d(c-d) ÷ (c²+d²)/(c-d) =
= ( (c-d)² +2cd) /d(c-d) × (c-d)/(c² +d²) =
= (c² -2cd+d²+2cd)/ (d×1) × 1/(c²+d²) =
= (c² + d²) / d(c² +d²) = 1/d
д)
(v+3) / (1-v) + (v+3)/(v-1) * (v+1) =
= (v+3)/ (- (v-1) ) + (v+3)(v+1) / (v-1) =
= - (v+3)/(v-1) + (v+3)(v+1)/(v-1) =
= ( -v - 3 + v² + v + 3v + 3) / (v-1) =
= ( v² +3v) / (v-1) =
= v(v+3)/(v-1)