№5. Вычислите: 1) 8 ⋅ 16⁻¹ = i) -5 ⋅ 9⁻² = 1) 4⁻¹ ⋅ 2⁻³ = -) 1 ⋅ 2⁰ – 1 ⋅ 2⁻¹ = _1) 10 – ($$\frac{1}{4}$$)$$^{-1}$$ = ) 36 + 0,2⁻² =

Краткое пояснение:

Для решения используем свойства степеней: $$a^{-n} = \frac{1}{a^n}$$, $$a^0=1$$, $$a^m \cdot a^n = a^{m+n}$$.

Пошаговое решение:

• 1) 8 ⋅ 16⁻¹
  8 ⋅ 16⁻¹ = 8 ⋅ $$\frac{1}{16}$$ = $$\frac{8}{16}$$ = $$\frac{1}{2}$$.
• i) -5 ⋅ 9⁻²
  -5 ⋅ 9⁻² = -5 ⋅ $$\frac{1}{9^2}$$ = -5 ⋅ $$\frac{1}{81}$$ = -$$\frac{5}{81}$$.
• 1) 4⁻¹ ⋅ 2⁻³
  4⁻¹ ⋅ 2⁻³ = $$\frac{1}{4}$$ ⋅ $$\frac{1}{2^3}$$ = $$\frac{1}{4}$$ ⋅ $$\frac{1}{8}$$ = $$\frac{1}{32}$$.
• -) 1 ⋅ 2⁰ – 1 ⋅ 2⁻¹
  1 ⋅ 2⁰ = 1 ⋅ 1 = 1.
  1 ⋅ 2⁻¹ = 1 ⋅ $$\frac{1}{2}$$ = $$\frac{1}{2}$$.
  1 - $$\frac{1}{2}$$ = $$\frac{1}{2}$$.
• _1) 10 – ($$\frac{1}{4}$$)$$^{-1}$$
  10 – ($$\frac{1}{4}$$)$$^{-1}$$ = 10 – 4 = 6.
• ) 36 + 0,2⁻²
  0,2 = $$\frac{1}{5}$$.
  0,2⁻² = $$(\frac{1}{5})^{-2} = 5^2 = 25$$.
  36 + 25 = 61.

Ответ:
1) $$\frac{1}{2}$$
i) -$$\frac{5}{81}$$
1) $$\frac{1}{32}$$
-) $$\frac{1}{2}$$
_1) 6
) 61