the number that gets multiplied when using exponents [example: 5³]

the form of a number written using a base and an exponent

the symbol that is used to represent roots [example: √ ]

the solution to a number that has been multiplied by itself twice 

[example: 5² = (5)(5) = 25]

the inverse of squaring a number [example: √25 = 5]

the solution to a number that has been multiplied by itself three times

[example: 5³ = (5)(5)(5) = 125]

the inverse of cubing a number [example: ∛125 = 5]

when multiplying two terms with the same base raised to an exponent, we can add the exponents [example: (x³)(x⁵) = x^{3 + 5} = x⁸]

if a base raised to a power is being raised to another power, the exponents are multiplied and the base remains the same [example: (x³)⁴ = x^{3 · 4} = x¹²]

when raising a product to a power, the power has to be distributed to each factor
[example: (2y)⁴ = (2⁴)(y⁴)]

any nonzero number raised to the power of 0 is equal to 1
[example: x⁰ = 1]

a way of writing very large or very small numbers in simpler forms by multiplying a number greater than or equal to 1 and less than 10 by powers of 10. 

[example: 12,457.21 = 1.245721 x 10³ and 0.2345 = 2.345 x 10^-1]

the notation in which we normally write numbers [example: 12,457.21]