An exponent is a number that indicates how many
times the base is to be used as a factor. Exponents indicate
repeated multiplication.
The base is the number that is multiplied.
Ex: Identify the base and the exponent: 2
3
Two is the base and three is the exponent.
2. Zero exponent:
Any number other than 0 raised to the zero power
is 1.
3. Order of operations:
When evaluating mathematical expressions,
we will perform operations in the following order:
First: If the expression contains grouping symbols, such as
parenthesis (), brackets [ ], braces { }, or a fraction bar, then
we perform the operations inside the grouping symbols, or
above and below the fraction bar, first.
Second: Evaluate, or simplify, any numbers with exponents.
Third: Do all multiplications and divisions in order from left to
right.
Fourth: Do all additions and subtractions in order from left to
right.
Ex: Simplify.
2 + 3•5
2 + 3•5
(operations of addition and multiplication are present)
= 2 + 15
(perform multiplication first)
= 17
(perform addition second)
b. 3 + 2•42
3 + 2•42
(operations of addition, mult, and exponentiation)
= 3 + 2•16
(do exponents first)
= 3 + 32
(do multplication second)
= 35
(do addition third)
4. Vocabulary:
We will now translate into mathematical symbols
English phrases that contain complicated expressions involving
the terms sum, product, difference, and quotient.
English phrase
Math symbols
sum of a and b
a + b
two times the sum of a and b
2(a + b)
product of p and q
p · q
product of p and the sum of a and b
p · (a + b)
sum of p and the product of a and
b
p + a · b
difference of p and the sum of a
and b
p - (a + b)
sum of the product of a and b and
the product of c and d
a · b + c
· d
Ex: Translate each phrase into math symbols.
a. product of 4 and the sum of 3 and x
Answer: 4 · (3 + x)
b. difference of 4 and the sum of 3 and x
Answer: 4 - (3 + x)
c. sum of the product of 4 and 3 and the product of 2 and
5
