361 lollipop candies or 697 gummy bear candies fills the bag of volume 528 in.³, which gives the following possible equation;
<h3>How can the correct equation be found?</h3>
Volume of candy bag = 528 in.³
Number of lollipop candies the bag can hold = 361 candies
Number of gummy bear candies the bag can hold = 697 candies
Therefore;
![1 \: lollipop = \frac{528}{361} = 1.46](https://tex.z-dn.net/?f=1%20%5C%3A%20lollipop%20%3D%20%20%5Cfrac%7B528%7D%7B361%7D%20%20%3D%20%201.46)
![1 \: gummy \: bear = \frac{528}{697} = 0.76](https://tex.z-dn.net/?f=1%20%5C%3A%20gummy%20%5C%3A%20bear%20%3D%20%20%5Cfrac%7B528%7D%7B697%7D%20%20%3D%20%200.76)
Which gives the following equation;
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The simplified expression of
is
.
Solution:
Given expression is
.
To simplify the given expression.
![$\Rightarrow4 x \cdot \frac{1}{x^{-5}} \cdot x^{-3}](https://tex.z-dn.net/?f=%24%5CRightarrow4%20x%20%5Ccdot%20%5Cfrac%7B1%7D%7Bx%5E%7B-5%7D%7D%20%5Ccdot%20x%5E%7B-3%7D)
Using exponent rule: ![\frac{1}{a^{-m}}=a^m](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Ba%5E%7B-m%7D%7D%3Da%5Em)
![$\Rightarrow4x \cdot x^{5}.x^{-3}](https://tex.z-dn.net/?f=%24%5CRightarrow4x%20%5Ccdot%20x%5E%7B5%7D.x%5E%7B-3%7D)
Using another exponent rule: ![a^m \cdot a^n=a^{m+n}](https://tex.z-dn.net/?f=a%5Em%20%5Ccdot%20a%5En%3Da%5E%7Bm%2Bn%7D)
![$\Rightarrow4x \cdot x^{5-3}](https://tex.z-dn.net/?f=%24%5CRightarrow4x%20%5Ccdot%20x%5E%7B5-3%7D)
![$\Rightarrow4x \cdot x^{2}](https://tex.z-dn.net/?f=%24%5CRightarrow4x%20%5Ccdot%20x%5E%7B2%7D)
Using exponent rule: ![a^m \cdot a^n=a^{m+n}](https://tex.z-dn.net/?f=a%5Em%20%5Ccdot%20a%5En%3Da%5E%7Bm%2Bn%7D)
![$\Rightarrow4x^{1+2}](https://tex.z-dn.net/?f=%24%5CRightarrow4x%5E%7B1%2B2%7D)
![$\Rightarrow4x^3](https://tex.z-dn.net/?f=%24%5CRightarrow4x%5E3)
Hence the simplified expression of
is
.
The correct answer would be c
Please urgent please help 1