evaluating algebraic expressions 4-1exponents exponential notation

Evaluating Algebraic Expressions

4-1 Exponents

Exponential Notation


4-1 Exponents

Exponent Essential Question:

How do we write numbers using exponents?


4-1 Exponents

Vocabulary

exponential form

exponent

base

power


4-1 Exponents

If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. 27 and 33 are equivalent.

7

ExponentBase

2


4-1 Exponents

Identify how many times 4 is a factor.4 • 4 • 4 • 4 = 44

Write in exponential form.

Additional Example 1: Writing Exponents

A. 4 • 4 • 4 • 4

Read (–6)3 as “–6 to the 3rd power" or "–6 cubed”.

Reading Math

Identify how many times –6 is a factor.

(–6) • (–6) • (–6) = (–6)3

B. (–6) • (–6) • (–6)


4-1 Exponents

Identify how many times 5 and d are each used as a factor.

Additional Example 1: Writing Exponents

C. 5 • 5 • d • d • d • d


5 • 5 • d • d • d • d = 52d4


4-1 Exponents

Identify how many times x is a factor.x • x • x • x • x = x5


Check It Out! Example 1

A. x • x • x • x • x

Identify how many times d is a factor.

d • d • d = d3

B. d • d • d


4-1 Exponents

Identify how many times 7 and b are each used as a factor.

7 • 7 • b • b = 72b2


C. 7 • 7 • b • b



4-1 Exponents

A. 35

= 243

35 = 3 • 3 • 3 • 3 • 3 Find the product.

Find the product.

B.

Simplify.

Additional Example 2: Simplifying Powers

= 1

27


4-1 Exponents

D. –28

= 256

–28 = –(2 • 2 • 2 • 2 • 2 • 2 • 2 • 2)

= –256

= (–4) • (–4) • (–4) • (–4) (–4)4

C. (–4)4

Simplify.

Additional Example 2: Simplifying Powers

Find the product.

Find the product. Then make the answer negative.


4-1 Exponents

The expression (–4)4 is not the same as the expression –44. Think of –44 as –1 ● 44. By the order of operations, you must evaluate the exponent before multiplying by –1.

Caution!


4-1 Exponents

A. 74

= 240174 = 7 • 7 • 7 • 7 Find the product.

Simplify.


Find the product.

B.

= 1 8


4-1 Exponents

D. –94

= 25

–94 = –(9 • 9 • 9 • 9)

= –6,561

= (–5) • (–5) (–5)2

C. (–5)2

Evaluate.

Find the product.

Find the product. Then make the answer negative.



4-1 Exponents

How do we use exponents within the order of operations?

Exponent Essential Question:


4-1 Exponents

The order in which mathematicians perform math problems.

a)Parenthesis – working inward outward

b)Exponentsc)Multiply or Divide – Left to Rightd)Add or Subtract – Left to Right

In the Order of Operations


4-1 Exponents

Mnemonic•Please

•Parenthesis•Excuse

•Exponents•My Dear

•Multiply or Divide – Left to Right•Aunt Sally

•Add or Subtract – Left to Right


4-1 Exponents

4 X 6 – (3 + 4) + 22

4 x 6 - 7 + 22

Parenthesis

Exponents

24 – 7 + 4

Multiply

4 X 6 – 7 + 4

Add or Subtract – Left to Right17 + 4

21


4-1 ExponentsAdditional Example 3: Using the Order of Operations

4(7) + 16

Substitute 4 for x, 2 for y, and 3 for z.

Simplify the powers.

Subtract inside the parentheses.

Multiply from left to right.

4(24 – 32) + 42

4(16 – 9) + 16

28 + 16

Evaluate x(yx – zy) + x for x = 4, y = 2, and z = 3.

y

x(yx – zy) + xy

Add. 44


4-1 ExponentsCheck It Out! Example 3

60 – 7(7)

Substitute 5 for x, 2 for y, and 60 for z.

Simplify the powers.


Multiply from left to right.

60 – 7(25 – 52)

60 – 7(32 – 25)

60 – 49

Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60.z – 7(2x – xy)

Subtract. 11


4-1 Exponents

(42 – 3 • 4)1

2


Simplify inside the parentheses.

Multiply

Substitute the number of sides for n.


2 diagonals

(16 – 12)1

2

(n2 – 3n)1

2

(4)1

2

Use the expression (n2 – 3n) to find the number of diagonals in a 4-sided figure.

1 2

evaluating algebraic expressions 4-1exponents exponential notation

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