Copyright\begin{matrix}c \\ ◯ \end{matrix}1999 ONG TCV Scoala Virtuala a Tanarului Matematician http://math.ournet.md 1

Степени

1. (a ± b)^{2} = a^{2} ± 2ab + b^{2}.

2. a^{2} − b^{2} = (a + b)(a − b).

3. (a ± b)^{3} = a^{3} ± 3a^{2}b + 3ab^{2} ± b^{3} = a^{3} ± b^{3} ± 3ab(a ± b).

4. a^{3} ± b^{3} = (a ± b)(a^{2} ∓ ab + b^{2}).

5. (a_{1}a_{2} … a_{m})^{n} = a_{1}^{n}a_{2}^{n} … a_{m}^{n} m, n ∈ N, a_{i} ≥ 0, i = \overline{1, n}.

6. a^{n_{1}}a^{n_{2}} … a^{n_{m}} = a^{n_{1}+n_{2}+...+n_{m}} m, n ∈ N, a ≥ 0.

7. \frac{a^{m}}{a^{n}} = a^{m−n} m, n ∈ N, a > 0.

8. (a^{m})^{n} = a^{m·n} m, n ∈ N, a > 0.

9. a^{−n} = \frac{1}{a^{n}} n ∈ N, a > 0.

10. a^{\frac{m}{n}} = ^{n} \sqrt{a^{m}} m, n ∈ N, n ≥ 2.

11. ^{n} \sqrt{a^{m}} = \{ \begin{matrix}a^{\frac{m}{n}} , если m = 2k + 1 \\ |a|^{\frac{m}{n}} , если m = 2k \end{matrix} k, m, n ∈ N, n ≥ 2.

12. ( ^{n} \sqrt{a})^{m} = ^{n} \sqrt{a^{m}} m, n ∈ N, n ≥ 2.

13. ^{n} \sqrt{a_{1}a_{2} … a_{m}} = ^{n} \sqrt{|a_{1}|} ^{n} \sqrt{|a_{2}|} … ^{n} \sqrt{|a_{m}|} m, n ∈ N, n ≥ 2.

14. ^{n} \sqrt{\frac{a}{b}} = \begin{matrix}^{n} & \sqrt{|a|} \\ ^{n} & \sqrt{|b|} \end{matrix} (b ≠ 0). ( ^{n} \sqrt{a + b} ≠ ^{n} \sqrt{a} + ^{n} \sqrt{b}, a ≠ 0, b ≠ 0). n ∈ N, n ≥ 2.