Jessica took $72 with her to buy books and manga at Barnes and Noble for her and her friends. The price for each book is $18. The price of each manga is one-third the price of a book. 1.) Sketch the graph that represents the situation and label the axes with the real-world items you are comparing.

2.) What do the intercepts of your graphed function mean in context of the problem? Explain both intercepts.

3.) If Jessica spends all her money on both books and manga, what is one example of the number of each she can buy.

4.) Prove algebraically that your above example in 3.) is true.

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: