Exponents and Order of Operations
1. Exponents:
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
Answer: 4 · 3 + 2
· 5
d. twice the product of 4 and x
Answer: 2 · (4
· x)
e. twice the sum of 8 and 5
2 · (8 + 5)
|
