Jasmine has 5 books that she wants to read. she wants to read the nonfiction book first and the mystery book last. in how many different orders can she read the books?

We have been given that Jasmine has 5 books and she wants to read the nonfiction book first and the mystery book last. It means that the time of reading of 2 books are fixed. Now she has 3 books which she needs to arrange.

Now, we know that n different things can be arranged in n! ways. We can use this concept to find the number of different orders can she read the books.

Using the above concept, 3 books can be arranged in 3! ways.

Therefore, there are 6 different orders in which she can read the books.

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: