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# 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 + 3â€¢5

 2 + 3â€¢5 (operations of addition and multiplication are present) = 2 + 15 (perform multiplication first) = 17 (perform addition second)

b. 3 + 2â€¢42

 3 + 2â€¢42 (operations of addition, mult, and exponentiation) = 3 + 2â€¢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 Â· q product of p and the sum of a and b p Â· (a + b) sum of p and the product of a and b p + a Â· 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 Â· b + c Â· d

Ex: Translate each phrase into math symbols.

a. product of 4 and the sum of 3 and x

Answer: 4 Â· (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 Â· 3 + 2 Â· 5

d. twice the product of 4 and x

Answer: 2 Â· (4 Â· x)

e. twice the sum of 8 and 5

2 Â· (8 + 5)