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zero exponent

It's value is always 1.

negative exponent

Means to write the reciprocal of the base and use a positive exponent

Scientific notation

where a number is written into 2 parts first just the digits (with decimal point after first digit) followed by ×10 to a power

Product of Powers Property

Example: 2² * 2³ = 2²⁺³

Power of a Power Property

I <i>a</i> is any nonzero real numbers and <i>n</i> is an integer, then <color red>(ab)ⁿ = aⁿbⁿ</color>.

Power of a Product Property

(ab)^x = a^x * b^x

Quotient of Powers Property

to divide powers WITH THE SAME NON ZERO BASE, subtract the exponents a^m/a^n = a^m-n

Positive Power of a Quotient Property

If <i>a</i> and <i>b</i> are nonzero real numbers and <i>n</i> is a positive integer, then <color red>(a/b)ⁿ = aⁿ/bⁿ</color>.

Negative Power of a Quotient Property

If <i>a</i> and <i>b</i> are nonzero real numbers and <i>n</i> is a positive integer, then <color red>(a/b)⁻ⁿ = (b/a)ⁿ = bⁿ/aⁿ</color>.

index

In the radical <i>ⁿ√x</i>, which represents the <i>n</i>th root of <i>x</i>, <i>n</i> is the index. In the radical √x, the index is understood to be 2.

<i>n</i>th root

The <i>n</i>th root of a number <i>a</i>, written as ⁿ√a or <i>a</i> ^(1/n), is a number that is equal to <i>a</i> when it is raised to the <i>n</i>th power.

b^(1/n)

A number raised to the power of 1/n is equal to the <i>n</i>th root of that number.

b^(m/n)

If <i>b</i> > 1 and <i>m</i> and <i>n</i> are integers, where <i>m</i> ≥ 1 and <i>n</i> ≥ 2, then b ^(m/n) = (ⁿ√b)^m = ⁿ√b^m.

monomial

a number or a product of numbers and variables with exponents that are whole numbers

Degree of a monomial

the sum of the exponents of the variables

polynomial

A monomial or sum of monomials

Degree of a polynomial

the degree of the term in the polynomial that has the highest degree

standard form of a polynomial

is written with terms from highest to lowest degree

leading coefficient

The coefficient of the term with the highest degree

quadratic polynomial

A polynomial of degree 2.

cubic polynomial

A polynomial of degree 3.

trinomial

A polynomial with 3 terms

binomial

A polynomial with two terms

root

A root of a polynomial in one variable is a value of the variable for which the polynomial is equal 0.

FOIL

To convert Factored Form to Standard Form you must

perfect-square trinomial

A trinomial whose factored form is the square of a binomial. A perfect-square trinomial has the form <i>a² − 2ab + b²</i> or <i>a² + 2ab + b²</i>.

difference of two squares

A polynomial of the form <i>a² − b²</i>, which may be written as the product <i>(a + b)(a − b)</i>.