Exponents

Indices or Exponents

Recall the definition for index or exponents.
Identify and use an index of a number.
Differentiate between expressions such as  $x^2$  and   $2x$  

Differentiate between  $x^{a\ }$ +  $x^b$   and  $x^{a\ }$  x   $x^b$  .
Establish and use the rule  $x^a$  x  $x^b$  =  $x^{a+b}$  
Establish and use the rule   $x^a$   $\div$   $x^b$  =  $x^{a-b}$  

Multiple Choice

2x and x² are these terms the same?

• Yes

• No

Multiple Select

What does 2x mean?

•  $x\times x$  

•  $x+x$  

•  $x^2$  

•  $2\times x$  

X^a + x^b

• What does x^a + x^b means ?

• Let us use x² + x³ as an example

• Recall that only like terms may be added or subtracted. Since both terms have different exponents this algebraic expression cannot be simplified any further.

Multiple Choice

Write the following in expanded form. 
10³

• 10+10+10
• 10x10x10
• 3x10
• 1,000

Multiple Choice

Write each product using an exponent. 
7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 

• 7⁷
• 7⁸
• 8⁷
• 7⁹

Multiple Choice

Write each product using an exponent. 
4 x 4 x 4 x 4 x 4 

• 4⁵
• 5⁴
• 4⁶
• 4⁶

 $x^a\times x^b$  

• Let us use  $x^{2\ }\times x^3$  as our example

• then we have  $x\times x\times x\times x\times x$  

• Count the number of times x is used in the multiplication as a factor.

• Express in exponent or index form is  $x^5$  

• We conclude that: $x^2\times x^3=x^{2+3\ }=x^5$ . This is the rule for multiplication

Multiple Choice

Simplify the expression: 
c⁴⋅c³=

• ^c12
• c⁴⁺³
• c⁷

Multiple Choice

In order to multiply powers with the same base, we add their exponents. 

• True 
• False

Multiple Choice

Simplify the expression: 3x²⋅x²=

• 3x
• 3x²⁺²
• 3x⁴

Multiple Choice

Simplify the expression x⁵x⁷

• x³⁵
• x¹²
• x²
• x^-2

Multiple Choice

Simplify (-7y²)(5y⁴)

• -35y⁶
• -2y⁶
• -35y⁸
• -2y⁸

Two lies and a truth.

• For the following slides identify the statement that is true.

Multiple Select

Identify the true statement.

• 2 x 2 x 2 = 6

• 2 x 2 x 2 = 8

• 2 x2 x 2 =10

Multiple Select

Identify the statement that is true

• 3² means 3 x 3

• 3² means 3 + 3

• 3² means 6

Multiple Select

Identify the statement which is true.

• (-3)² = 6

• (-3) ² = -9

• ( -3) ² = 9