$$a^2=a×a$$

$$a^1=a$$

$$a^0=1$$

$$a^{−1}=1/a$$

$$a^{−n}=1/{a^n}$$

$$a^m×a^n=a^m a^n=a^{(m+n)}$$

$${a^m}/{a^n}=a^{m−n}$$

$$(a^m)^n=a^{(m×n)}$$

$$a^{1/n}=√^{n}a$$

$$√^n{a}√^n{b} = √^n{ab}$$

$$√{ab} = √a×√b$$

$$(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2$$

$$(a−b)^2=(a−b)(a−b)=a^2−2ab+b^2$$

$$a^2−b^2=(a+b)(a−b)$$

$$(a+b)^3=a^3+3a^2b+3ab^2+b^3$$

$$(a−b)^3=a^3−3a^2b+3ab^2−b^3$$