Multiplication and Division Properties of Exponents

Quotient of a Powers Property

A power divided by another power with the same base is equal to the base raised to the difference of the exponents.

Product of Powers Property

A power multiplied by another power with the same base is equal to the base raised to the sum of the exponents.

Power of a Power Property

A power raised to another power is equal to the base raised to the product of the exponents.

Negative Power of a Quotient Property

A quotient raised to a negative power is equal to the reciprocal of the quotient raised to the opposite power.

Positive Power of a Quotient Property

A quotient raised to a positive power equals the quotient of each base raised to that power.

Power of a Product Property

To find a power of a product, find the power of each factor and multiply

scientific notation

a method of writing very large or very small numbers in the form of a number equal to or greater than 1 and less than 10 multiplied by a power of ten

exponent

a symbol or number that indicates the power to which a base is raised

exponential expression

an algebraic expression that contains at least one term containing an exponent

integer exponent

an exponent consisting of any positive number with no fractional part, any negative number with no fractional part, or zero

power of ten

an exponential expression with ten as the base

Exponential Expression

an expression that contains at least one term containing an exponent

power

the number of times a base is multiplied by itself indicated by an exponent

base

the value being raised to a power