Math Rules Flashcards
If you ADD OR SUBTRACT exponent terms with the same base, then you….
2^3 + 2^5
Pull out the common factor
2^3 (1+2^2)
If you ADD OR SUBTRACT exponent terms with different bases, then you…
2^3 + 6^3
Break down the bases and THEN pull out the common factor
2^3 + (2^3x3^3) –> 2^3(1+3^3)
If you SQUARE a SQUARE ROOT you get…
The original number being squared/rooted
If you square root a square, you get…
The positive value of the original number
Square Root of a number X (where X is greater than 1) will be BIGGER OR SMALLER than X?
Smaller
Square root of a number X where X is between 0 and 1 will be BIGGER or SMALLER than X?
Bigger
If you take the square root of 1 or 0, you get….
The number you started with (1 or 0)
A square root is equivalent to an exponent of….
1/2, for exponents with positive bases
To take the square root of a positive number that is raised to a power, you…
Root (5^12)
Rewrite the square as an exponent of 1/2, then multiply the exponents
(5^12)^1/2 = 5^6
Square root of a negative number?
Is in an imaginary number - can’t take the square root
Cube root of a negative number is….
A negative number
A cube root is equivalent to an exponent of …
1/3
Dealing with fractional exponents. You:
8^2/3
Apply two exponents: the numerator as a power and the denominator as a fractional root, in whatever order seems easiest
(8^2)^1/3 –> Cube root 64 –> 4
To multiply or divide square roots, you…
Put everything under the root and then simplify
Further simplify a square root that is not a perfect square by…
Root 12
Factoring out squares.
Root 12 can be simplified further:
12 = 4 x 3, and 4 is a perfect square
Root 12 = Root (4x3) = Root 4 x Root 3
2 root 3 = Root 12
If you need to simplify a square root and you don’t spot a perfect square…
Root 360
Break the number down into its prime factorization (will take longer but works):
360 –> 2 x 2 x 2 x 3 x 3 x 5
Root 360 = 2x3 Root (2x5) = 6 Root 10
To add or subtract under the root, you…
Root (3^2 + 4^2)
Crunch the numbers, if they’re small, OR Pull out common square factors
YOU CANNOT BREAK THIS INTO ROOT 3^2 + ROOT 4^2 –> CAN ONLY DO THAT WITH MULTIPLICATION
Root (4^14 + 4^16) =
If you MULTIPLY exponential terms with the same base… then you
X^2 x x^3
Add the exponents
X^2 x X^3 = X ^ 5
If you DIVIDE exponential terms with the same base, then you . . .
(A^5)
______
(A ^3)
Subtract the exponents
A ^ 5
______
A ^ 3
=
A^2
Raise anything to the power of zero, besides zero itself, you get a ….
1
Raise a zero to a negative power, you get a ….
Impossible number
Raise anything else to a negative power, get a
A ^ -2
1 over the same number to a corresponding positive power
A ^ -2 = 1 / a^2
To move a term from the numerator or denominator of a fraction, you…
(2a^-2)/3 =
Switch the positive or negative sign
(2a^-2)/3 = 2/3a^2
If you raise something to two successive powers…
(A^2)^4
Multiply the powers
(a^2)^4 = a^8
To apply an exponent to a product
(ab)^3
Apply the exponent to each factor of the product
Ab)^3 = (a^3)(b^3
To apply an exponent to an entire fraction…
(a/b)^4
Apply the exponent separately to the top and the bottom
(a/b)^4 = a^4/b^4
If you see two factors with the same exponent, you might…
a^3 x b^3
Regroup the factors as a product
a^3 x b^3 = (ab)^3
To add or subtract terms with the same base, you…
2^3 + 2^5
Pull out the common factor
2^3 + 2^5 –> 2^3 (1+2^2)
To add or subtract terms with different bases…
2^3 + 6^3
Break down the bases and pull out the common factor
2^3 + 6^3 –> 2^3 + (2^3x3^3) –> 2^3(1+3^3)
