Question | Answer |
Zero Exponent | Any nonzero number raised to the zero power is 1 |
Negative Exponent | A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the corresponding positive exponent. |
Scientific Notation | a method of writing numbers that are very large or very small in two parts - a number between 1 & 10 that is multiplied by ten raised to a positive or negative power |
An exponential expression is completely simplified if... | 1) there are no negative exponents
2) the same base does not appear more than once in a product or quotient
3) no powers, products or quotients are raised to powers
4) numerical coefficients in a quotient do not have any common factor other than 1 |
Product of Powers Property | The product of two powers with the same base equals that base raised to the sum of the powers |
Power of a Power Property | A power raised to another power equals that base raised to the product of the exponents |
Power of a Product Property | A product raised to a power equals the product of each factor raised to that power |
Quotient of Powers Property | The quotient of two nonzero powers with the same base equals to base raised to the difference of the exponents |
Positive Power of a Quotient Property | A quotient raised to a positive power equals the quotient of of each base raised to that power |
Negative Power of a Quotient Property | A quotient raised to a negative power equals the reciprocal of the quotient raised to the opposite (positive) power |
Root Index | the small number to the left of the radical symbol that tells you which root to take - 2 would be square root, 3 would be cube root, etc. |
Factional Exponent 1/n | A number raised to the power of 1/n is equal to the "n"th root of that number |
Factional Exponent m/n | A number raised to the power of m/n is equal to the "n"th root of the number raised to the "m"th power |
Monomial | A number, a variable or a product of numbers and variables with whole-number exponents |
Degree of a Monomial | The sum of the exponents of the variables in a monomial |
Polynomial | A monomial or a sum or difference of monomials |
Degree of a Polynomial | The degree of the of the term with the greatest degree |
Standard Form of a Polynomial | Contains one variable and is written in with the terms in order from greatest degree to least degree |
Leading Coefficient | When written in standard form, it is the coefficient of the first term |
Linear Polynomial | Polynomial with the degree of 1 |
Quadratic Polynomial | Polynomial with the degree of 2 |
Cubic Polynomial | Polynomial with the degree of 3 |
Binomial | Polynomial with two terms |
Trinomial | A polynomial with three terms |
FOIL | A method for multiplying binomials:
F - multiply first terms
O - multiply outside terms
I - multiply inside terms
L - multiply last terms |
Perfect Square Trinomial | A trinomial that results from squaring a binomial |