CalcWorkshop: Exponents

a^0

1 (anything to the power 0 = 1)

a^1

a

a^n

to the nth power, n times

all things in the parenthesis are...

affected by the exponent

if the sign is outside of the parenthesis...

only the number is affected, not the sign

multiplying with like bases

keep the base, add the exponents

monomial

one term

polynomial

one or more terms or four or more terms

monomial exponents are

nonnegative integers

How to add exponents

put exponents and coefficients as needed, combine like terms, simplify, add exponents

When can you not add/subtract exponents?

When adding/subtracting bases

power of a power

(a^m)^n = a^mn

power of a product

(ab)^m = a^m b^m

(a^m b^n)^p

a^mp b^np

a^m * a^n

a^m+n

a^m/a^n

a^m-n

(a/b)^n

a^n/b^n

(a^m/b^n)^p

a^mp/b^np

(a^1)^n+1

a^n+1 (distribute the one exponent into n + 1)

dividing exponents with like bases

keep the base, subtract the exponents

rule for negative exponents

a^-n = 1/a^n or 1/a^-n = a^n/1

scientific notation

used to write very large and small numbers

parts of scientific notation

digit term (1-9) x exponential term

How many digits are to the left of a decimal in scientific notation?

one digit

scientific notation to standard notation

10^n: move n places to the right
10^-n: move n places to the left

standard notation to scientific notation

10^n: if the decimal moves left
10^-n: if the decimal moves right

How to multiply scientific notation

multiply the coefficients and add the exponents

How to divide scientific notation

divide the coefficients and subtract the exponents

0^0, 0/0

indeterminate

1/0

undefined

How to multiply exponents with different bases

multiply (group the numbers), keep the exponents

a^m b^m

(ab)^m

How to multiply exponents with different powers and bases

no simplification

How to divide exponents with different bases

divide bases, keep the exponents

a^m/b^m

(a/b)^m

How to divide exponents with different powers and bases

no simplification