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21.
Cube of sum
$(a+b)^3=a^3+3a^2b+3ab^2+b^3$
Polynomial
Power
22.
Fourth power of difference
$(a-b)^4=a^4-4a^3b+6a^2b^2-4ab^3+b^4$
Polynomial
Power
23.
Fourth power of sum
$(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4$
Polynomial
Power
24.
Multiplication rule
$a^m \cdot a^n=a^{m+n}$
Exponents
25.
Zero exponent
$a^0=1$
Exponents
26.
Division Rule
$\dfrac{a^m}{a^n}=a^{m-n}$
Exponents
27.
Power of power rule
$\left(a^n\right)^m=a^{nm}$
Exponents
28.
Negative exponent
$a^{-n}=\dfrac{1}{a^n}$
Exponents
29.
Negative exponent of a fraction
$\left(\dfrac{a}{b}\right)^{-n} = \left(\dfrac{b}{a}\right)^n$
Exponents
30.
Power of a product
$\left(ab\right)^n=a^n b^n$
Exponents
31.
Power of a fraction
$\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}$
Exponents
32.
Root of a product
$\sqrt[n]{ab}=\sqrt[n]{a} \cdot \sqrt[n]{b}$
Root
33.
Root of a fraction
$\sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$
Root
34.
Product of roots
$\sqrt[n]{a} \cdot \sqrt[m]{b} = \sqrt[mn]{a^mb^n}$
Root
35.
Quotione of roots
$\dfrac{\sqrt[n]{a}}{\sqrt[m]{b}}=\sqrt[nm]{\dfrac{a^m}{b^n}}$
Root
36.
Power of a root
$\left(\sqrt[n]{a^m}\right)^p=\sqrt[n]{a^{mp}}$
Root
37.
$\left(\sqrt[n]{a}\right)^n=a$
Root
38.
$\sqrt[n]{a^m}=\sqrt[np]{a^{mp}}$
Root
39.
$\sqrt[n]{a^m}=a^{\frac{m}{n}}$
Root
40.
Root of a root
$\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$
Root

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