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Pneumonic – Please Excuse My Dear Aunt Sally
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction |
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Rule 1: To multiply numbers with the same base, add the exponents and keep the base the same.
aman = am+n
Rule 2: When raising a power of a number to a power, multiply the exponents and keep the base the same.
(am)n = amn
Rule 3: When dividing two exponential numbers, subtract the powers.
am/an = am-n
Rule 4: Any exponential number divided by itself is equal to one.
an/an = 1
Rule 5: To raise a product to a power, raise each factor to that power.
(ab)n = anbn
Rule 6: To raise a quotient to a power, raise both the numerator and denominator to that power.
(a/b)n = an/bn |
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Common prefixes:
Pico x10-12
Nano x10-9
Micro x10-6
Milli x10-3
Kilo x103
Mega x106
Giga x109 |
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• Multiply quantity outside parentheses by both quantities inside parentheses, and simplify.
• If two groups are multiplied together, and each group has two terms added together, use FOIL method:
F – Multiply First term of each group
O – Multiply two outer terms together
I – Multiply two inner terms together
L – Multiply two last terms together |
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• Goal is to isolate the variable on one side of the equation, and all other terms on the other.
Pneumonic – Remember My Education Is For Driving Reactors Carefully
• Reduce any fraction
• Multiply both sides by LCD
• Expand any powers
• Isolate the unknown
• Factor if appropriate
• Divide by any coefficients
• Reduce
• Check |
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• A logarithm is an exponent.
• It is a power (x) that a number, called the base (b), must be raised to in order to produce another number, (y). Put another way, x is the logarithm of the number y to the base b.
• If bx = y, then x = logb(y). “x” is called the logarithm of “y” to the base “b”. |
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• logb(A) = x is the same as bx = A
• logb(AB) = logb(A) + logb(B)
• logb(A/B) = logb(A) - logb(B)
• logb(An) = n•logb(A)
• logb(A1/n) = logb(n√A ) = 1/n logb(A)
• logb(1/A) = logb(A-1) = -logb(A)
• log(1) = ln(1) = 0 (since any number, other then 0, raised to the zero power = 1)
• ln(e) = 1
• log(10) = 1 |
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Trigonometric Relationships |
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