№4. Найдите значение выражения: a) 6 ⋅ 3⁻⁴ = б) -3 ⋅ 10⁻⁴ = в) 24 ⋅ (-8)⁻¹ = г) 12 ⋅ (-$$\frac{1}{4}$$)² = ж) 0,2⁻² + ($$\frac{1}{4}$$)-³ = 3) 0,5⁰ + 0,2⁻⁴ =

Краткое пояснение:

При решении будем использовать свойства степеней: $$a^{-n} = \frac{1}{a^n}$$, $$a^0 = 1$$, $$(ab)^n = a^n b^n$$, $$(\frac{a}{b})^n = \frac{a^n}{b^n}$$.

Пошаговое решение:

• а) 6 ⋅ 3⁻⁴
  6 ⋅ 3⁻⁴ = 6 ⋅ $$\frac{1}{3^4}$$ = 6 ⋅ $$\frac{1}{81}$$ = $$\frac{6}{81}$$ = $$\frac{2}{27}$$.
• б) -3 ⋅ 10⁻⁴
  -3 ⋅ 10⁻⁴ = -3 ⋅ $$\frac{1}{10^4}$$ = -3 ⋅ $$\frac{1}{10000}$$ = -$$\frac{3}{10000}$$.
• в) 24 ⋅ (-8)⁻¹
  24 ⋅ (-8)⁻¹ = 24 ⋅ $$\frac{1}{-8}$$ = -$$\frac{24}{8}$$ = -3.
• г) 12 ⋅ (-$$\frac{1}{4}$$)⁻²
  12 ⋅ (-$$\frac{1}{4}$$)$$^{-2}$$ = 12 ⋅ $$(-4)^2$$ = 12 ⋅ 16 = 192.
• ж) 0,2⁻² + ($$\frac{1}{4}$$)$$^{-3}$$
  0,2 = $$\frac{1}{5}$$.
  $$\left(\frac{1}{5}\right)^{-2} + \left(\frac{1}{4}\right)^{-3}$$ = $$5^2 + 4^3$$ = 25 + 64 = 89.
• 3) 0,5⁰ + 0,2⁻⁴
  0,5⁰ = 1.
  0,2 = $$\frac{1}{5}$$.
  0,2⁻⁴ = $$\left(\frac{1}{5}\right)^{-4} = 5^4 = 625$$.
  1 + 625 = 626.

Ответ:
а) $$\frac{2}{27}$$
б) -$$\frac{3}{10000}$$
в) -3
г) 192
ж) 89
3) 626