3. Tyler decides which type of pizza to order. The choices for crust are thin crust or regular crust. The choices for one topping are pepperoni, mushrooms, olives, sausage, or green peppers. Tyler has trouble deciding because there are so many possibilities. He selects the type of crust and one topping at random. How many outcomes are in the sample space?

10 outcomes

Step-by-step explanation:

To solve the question above, we use the fundamental counting principle

We have two events,

Event A = Type of crust = 2 types

The choices for crust are thin crust or regular crust.

Event B = Types of topping = 5 toppings

The choices for one topping are pepperoni, mushrooms, olives, sausage, or green peppers.

According to fundamental counting principles, the number of possible outcomes that are in the sample space is : Event A × Event B

= 2 × 5 = 10 outcomes

=

a negative exponent is translated as follows:

so, we have

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: