Exponents/Polynomials

Power of a Power

(a²)³=a⁶ To find the power of a power, simply multiply the exponents.

coefficient

the number in front of the variable

3x⁶ , Which is the BASE? The 3, the x or the 6?

The BASE is the number or variable that has an exponent. The BASE is x

3x⁶ , Which is the Coefficient? The 3, the x or the 6?

The COEFFICIENT is the number in front of the BASE. The COEFFICIENT is 3.

3x⁶ , Which is the Exponent? The 3, the x or the 6?

The EXPONENT is the raised number to the right of the BASE. The EXPONENT is 6.

polynomial

a monomial or the sum or difference of monomials

linear

a polynomial with a degree of 1

quadratic

a polynomial with a degree of 2

cubic

a polynomial with a degree of 3

constant

a polynomial with a degree of zero, so it is just a number ; for example, 5 or 10 or -4 or 3.5

monomial

an expression with only one term

trinomial

an expression with three terms

binomial

an expression with two terms

Power of a Product

a² × b² = (ab)² To multiply two numbers with the same exponent, multiply the bases first, then raise the result to the shared power (as long as a, b, and the exponent aren't 0)

Quotient of Powers

a²/a¹=a¹ To divide two powers with the same base, subtract the exponents.

Power of a Quotient

a²/b² = (a/b)² To divide two numbers with the same exponent, divide the bases first then raise that to the shared power (as long as a, b, and the exponent aren't 0)

Product of Powers

a¹ × a² = a³ To multiply two powers with the same base, add the exponents.

Zero Exponents

a⁰=1 Any number not equal to zero, raised to a power of 0 is 1.

Negative Exponents

a⁻ⁿ=1/aⁿ Any number not equal to zero raised to a negative power is 1 divided by the same positive power

leading coefficient

coefficient of the first term when the polynomial is in standard form

standard form of a polynomial

terms are arranged from the largest degree to the smallest degree

base

the factor in an exponential expression, the number that is being repeatedly multiplied.

degree of a polynomial

the greatest degree of any TERM in the polynomial

exponent

the number raised to the right of the base, tells the base how many times to be a factor