R.3 Properties Of Exponents Flashcards
Power property of exponents
(x^m)^n = x^(m*n)
To raise an exponential term to a power, keep the same base and multiply the exponents
Product property of exponents
b^n * b^m = b^n+m
To multiply exponential forms with the same base, keep the common base and add the exponents.
Product to a power property
(a^m * b^n)^p = a^(mp) * b^(np)
To raise a product of exponential terms to a power, multiply every exponent inside the parentheses by the exponent outside the parentheses.
Quotient to a power property
(a^m / b^n)^p = (a^mp) / (b^np)
To raise a quotient of exponential terms to a power, multiply every exponent inside the parentheses by the exponent outside the parentheses.
Quotient property of exponents
(b^m) / (b^n) = b^(m-n)
To divide two exponential terms of the same base, subtract the exponent of the denominator from the exponent of the numerator.
Property of negative exponents
Write the power as a reciprocal:
x^(-n) = 1/x^n
(a/b)^-n = (b/a)^n
1/(b^-n) = b^n
Zero exponent property
Any base be != 0, b^0 = 1
Scientific Notation
for N where 1 < 10 and k is an integer
N * 10^k
Monomial
A term using only whole number exponents, with no variables in the deonominator
Degree of a monomial
The sum of exponents occurring on variable factors.
Polynomial
A monomial, or any sum or difference of monomial terms.
How are polynomials classified?
By their degree and number of terms.
Binomial
A polynomial with two terms
Trinomial
A polynomial with three terms
What is the standard form of a polynomial expression?
The terms of the polynomial are written in descending order of degree, beginning with the highest degree term.
What is the coefficient of the highest degree term?
The leading coefficient.
How do you compute the product of a monomial and a polynomial?
The distributive property
How do you compute the produce of a binomial times a polynomial?
The distributive property:
a - b) (x + y + z) = a(x + y + z) - b(x + y + z
How do you compute the factor of two binomials?
The FOIL method.
First
Outer
Inner
Last
What is the pattern of the answers to a FOIL calculation?
The first term of the answer is the product of the first two terms from each binomial.
The last term is the product of the last two terms of the polynomials
The middle term is the sum of the outermost product and the innermost product.
describe a + b versus a - b
These are binomial conjugates
Define binomial conjugate
The same two terms with different signs between them.
What is the product of binomial conjugates?
The difference of two squares. For example:
(a + 7) * (a - 7) = a^2 - 49
or
(a + b) * (a - b) = a^2 - b^2
What is the result of a binomial squared?
(A + B)^2 = A^2 + 2AB + B^2
(A - B)^2 = A^2 - 2AB + B^2
