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.
