Alex is correct the book would cost $18.52 before taxes adding 10% tax the book would cost an additional $1.85 for a total of $20.37. This would be just under the $21.00 that both Alex and Laura had to spend. Laura tried to combined the 35% discount which you cannot do. So yes they both would be able to purchase the book.
Answer:

Step-by-step explanation:
![{x}^{ - 2} {y}^{3} \sqrt[3]{ 64{x}^{5} {y}^{3} } = a {x}^{b} {y}^{c} \\ \\ {x}^{ - 2} {y}^{3} \times 4 \times {x}^{ \frac{5}{3} } \times y= a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5}{3} - 2 } {y}^{3 + 1} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5 - 6}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{ - 1}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ a = 4 \\ \\ b = - \frac{1}{3} \\ \\ c = 4 \\ \\ abc = 4 \times ( - \frac{1}{3} ) \times 4 \\ \\ = 16 \times ( - \frac{1}{3} ) \\ \\ abc = - \frac{16}{3}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B%20-%202%7D%20%20%7By%7D%5E%7B3%7D%20%20%5Csqrt%5B3%5D%7B%2064%7Bx%7D%5E%7B5%7D%20%20%7By%7D%5E%7B3%7D%20%7D%20%20%3D%20a%20%7Bx%7D%5E%7Bb%7D%20%20%7By%7D%5E%7Bc%7D%20%20%5C%5C%20%20%5C%5C%20%20%7Bx%7D%5E%7B%20-%202%7D%20%20%7By%7D%5E%7B3%7D%20%20%20%5Ctimes%204%20%5Ctimes%20%20%7Bx%7D%5E%7B%20%5Cfrac%7B5%7D%7B3%7D%20%7D%20%20%20%5Ctimes%20y%3D%20a%20%7Bx%7D%5E%7Bb%7D%20%20%7By%7D%5E%7Bc%7D%20%20%20%5C%5C%20%20%5C%5C%204%20%7Bx%7D%5E%7B%20%5Cfrac%7B5%7D%7B3%7D%20-%202%20%7D%20%20%7By%7D%5E%7B3%20%2B%201%7D%20%20%3D%20a%20%7Bx%7D%5E%7Bb%7D%20%20%7By%7D%5E%7Bc%7D%20%20%20%5C%5C%20%20%5C%5C%204%20%7Bx%7D%5E%7B%20%5Cfrac%7B5%20-%206%7D%7B3%7D%20%7D%20%20%7By%7D%5E%7B4%7D%20%20%3D%20a%20%7Bx%7D%5E%7Bb%7D%20%20%7By%7D%5E%7Bc%7D%20%20%20%5C%5C%20%20%5C%5C%204%20%7Bx%7D%5E%7B%20%5Cfrac%7B%20-%201%7D%7B3%7D%20%7D%20%20%7By%7D%5E%7B4%7D%20%20%3D%20a%20%7Bx%7D%5E%7Bb%7D%20%20%7By%7D%5E%7Bc%7D%20%20%20%5C%5C%20%20%5C%5C%20equating%20%5C%3A%20like%20%5C%3A%20terms%20%5C%3A%20on%20%5C%3A%20both%20%5C%3A%20sides%20%5C%5C%20%20%5C%5C%20a%20%3D%204%20%5C%5C%20%20%5C%5C%20b%20%3D%20%20%20-%20%5Cfrac%7B1%7D%7B3%7D%20%20%5C%5C%20%20%5C%5C%20c%20%3D%204%20%5C%5C%20%20%5C%5C%20abc%20%3D%204%20%5Ctimes%20%28%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%5Ctimes%204%20%5C%5C%20%20%5C%5C%20%20%3D%2016%20%5Ctimes%20%28%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%5C%5C%20%20%5C%5C%20abc%20%3D%20%20-%20%20%5Cfrac%7B16%7D%7B3%7D%20)
A I think I’m not 100 sure
Answer:
The exact answer in terms of radicals is ![x = 5*\sqrt[3]{25}](https://tex.z-dn.net/?f=x%20%3D%205%2A%5Csqrt%5B3%5D%7B25%7D)
The approximate answer is
(accurate to 5 decimal places)
===============================================
Work Shown:
Let ![y = \sqrt[5]{x^3}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B5%5D%7Bx%5E3%7D)
So the equation reduces to -7 = 8-3y
Let's solve for y
-7 = 8-3y
8-3y = -7
-3y = -7-8 ... subtract 8 from both sides
-3y = -15
y = -15/(-3) ... divide both sides by -3
y = 5
-----------
Since
and y = 5, this means we can equate the two expressions and solve for x

![\sqrt[5]{x^3} = 5](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E3%7D%20%3D%205)
Raise both sides to the 5th power

Apply cube root to both sides
![x = \sqrt[3]{125*25}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B125%2A25%7D)
![x = \sqrt[3]{125}*\sqrt[3]{25}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B125%7D%2A%5Csqrt%5B3%5D%7B25%7D)
![x = \sqrt[3]{5^3}*\sqrt[3]{25}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B5%5E3%7D%2A%5Csqrt%5B3%5D%7B25%7D)
![x = 5*\sqrt[3]{25}](https://tex.z-dn.net/?f=x%20%3D%205%2A%5Csqrt%5B3%5D%7B25%7D)
