Answer: (y^{2}x^{3}⋅5)/4
Step-by-step explanation:
Convert to Radical Form
![(5x^3y^2)\frac{2}{8}](https://tex.z-dn.net/?f=%285x%5E3y%5E2%29%5Cfrac%7B2%7D%7B8%7D)
Reduce the expression
by cancelling the common factors.
Factor 2 out of 2.
![5x^3y^2\frac{2(1)}{8}](https://tex.z-dn.net/?f=5x%5E3y%5E2%5Cfrac%7B2%281%29%7D%7B8%7D)
Factor 2 out of 8.
![5x^3y^2 \frac{2(1)}{2(4)}](https://tex.z-dn.net/?f=5x%5E3y%5E2%20%5Cfrac%7B2%281%29%7D%7B2%284%29%7D)
Cancel the common factor.
![5x^3y^2 \frac{1}{4}](https://tex.z-dn.net/?f=5x%5E3y%5E2%20%5Cfrac%7B1%7D%7B4%7D)
Combine 5 and
.
![x^3y^2\frac{5}{4}](https://tex.z-dn.net/?f=x%5E3y%5E2%5Cfrac%7B5%7D%7B4%7D)
Combine
and
.
![y^2\frac{x^3(5)}{4}](https://tex.z-dn.net/?f=y%5E2%5Cfrac%7Bx%5E3%285%29%7D%7B4%7D)
Combine
and ![\frac{x^3*5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%2A5%7D%7B4%7D)
![\frac{y^2x^3*5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7By%5E2x%5E3%2A5%7D%7B4%7D)
Use distributive property
4(x-3) = 4x-12
2x-6 + 4x - 12
Combine like term
6x - 18
Answer:
8 movies and 6 video games
<em></em>
Step-by-step explanation:
Given
![Gift\ Card = \$600](https://tex.z-dn.net/?f=Gift%5C%20Card%20%3D%20%5C%24600)
![Movies =\ $20](https://tex.z-dn.net/?f=Movies%20%3D%5C%20%2420)
![Video\ Game = \$50](https://tex.z-dn.net/?f=Video%5C%20Game%20%3D%20%5C%2450)
![Minimum\ Items = 13](https://tex.z-dn.net/?f=Minimum%5C%20Items%20%3D%2013)
Required
Determine the items Lonnie can afford
To solve this question, we make use of trial by error method by taking the options one at a time:
Option 1: 6 movies and 4 video games
<em>This option can not be considered because the number of items is not up to the minimum Lonnte must purchase.</em>
<em />
Option 2: 14 movies and 7 video games
![Cost = 14 * \$20 + 7 * \$50](https://tex.z-dn.net/?f=Cost%20%3D%2014%20%2A%20%5C%2420%20%2B%207%20%2A%20%5C%2450)
![Cost = \$280 + \$350](https://tex.z-dn.net/?f=Cost%20%3D%20%5C%24280%20%2B%20%5C%24350)
![Cost = \$630](https://tex.z-dn.net/?f=Cost%20%3D%20%5C%24630)
<em>This option can not be considered because the cost of purchase is greater than Lonnte's worth of Gift card.</em>
<em />
Option 3: 2 movies and 10 video games
<em>This option can not be considered because the number of items is not up to the minimum Lonnte must purchase.</em>
<em />
Option 4: 8 movies and 6 video games
![Cost = 8 * \$20 + 6 * \$50](https://tex.z-dn.net/?f=Cost%20%3D%208%20%2A%20%5C%2420%20%2B%206%20%2A%20%5C%2450)
![Cost = \$160 + \$300](https://tex.z-dn.net/?f=Cost%20%3D%20%5C%24160%20%2B%20%5C%24300)
![Cost = \$460](https://tex.z-dn.net/?f=Cost%20%3D%20%5C%24460)
Hence, the correct option is <em>8 movies and 6 video games
</em>