Summary of basic math properties

I know it’s better to have intuition rather than memorize formulas and rues. But nonetheless, I want to combine the most common math properties and formulas that pop up in everyday life and work in one place for quick access. Please let me know in case if I missed something.

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Properties of Exponents

Property Formula
Zero to the Power of Zero 00 is undefined.
Zero Exponent Property a0 = 1‚ (a ≠ 0)
Negative Exponent Property a-b = 1⁄ab‚ (a ≠ 0)
Product of Powers Property ab + ac = a(b+c)‚ (a ≠ 0)
Quotient of Powers Property ab⁄ac = a(b-c) ‚ (a ≠ 0)
Power of a Product Property ac * bc = (a*b)c ‚ (a‚b ≠ 0)
Power of a Quotient Property ac⁄bc = (a⁄b)c‚ (a‚b ≠ 0)
Power of a Power Property (ab)c = a(b*c)
Rational Exponent Property radical_rule

Logarithm Properties

Property Formula
Product Rule log_rule_1
Quotient Rule log_rule_2
Power Rule log_rule_3
Equality Rule log_rule_4

Trigonometric Identities

Property Formula
Reciprocal Identities recip_ident
Pythagorean Identities pyth_ident
Quotient Identities Quotient_ident
The Sum and Difference Formulas sum_diff_ident
Co-Function Identities complements_ident
Even-Odd Identities nega_ident
Double Angle Formulas dbl_angl_ident

Statistics

Standard_deviation_diagram

Property Formula
Variance variance
Standard Deviation std_dev
Sample Standard Deviation  samp_std_dev

Basic Integration and Differentiation Rules

Differentiation rule Integration rule
id_rule_1_l id_rule_1_r
id_rule_2_l  id_rule_2_r
id_rule_3_l id_rule_3_r
id_rule_4_l  id_rule_4_r
id_rule_5_l  id_rule_5_r
id_rule_6_l id_rule_6_r
id_rule_7_l id_rule_7_r
id_rule_8_l id_rule_8_r
id_rule_9_l id_rule_9_r
id_rule_10_l  id_rule_10_r
id_rule_11_l  id_rule_11_r
id_rule_12_l  id_rule_12_r
id_rule_13_l id_rule_13_r

Misc

Property Formula
Quadratic Formula quadratic_form
Euler's Formula Eulersformula2

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