Answer:
Step-by-step explanation:
The given expression: ![4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}}](https://tex.z-dn.net/?f=4%20%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D%20%5Ccdot%20y%5E%7B4%7D%20%5Ccdot%20%5Csqrt%7Bx%7D%20%5Ccdot%20%5Csqrt%5B3%5D%7By%5E%7B5%7D%7D)
Step 1: Change radical to fractional exponent.
Formula for fractional exponent: ![\sqrt[n]{a}=a^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%3Da%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
The power to which the base is raised becomes the numerator and the root becomes the denominator.
Step 2: Apply law of exponent for a product 
Multiply powers with same base.
Take LCM for the fractions in the power.
Hence the simplified form of ![4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}} \text { is } 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}](https://tex.z-dn.net/?f=4%20%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D%20%5Ccdot%20y%5E%7B4%7D%20%5Ccdot%20%5Csqrt%7Bx%7D%20%5Ccdot%20%5Csqrt%5B3%5D%7By%5E%7B5%7D%7D%20%5Ctext%20%7B%20is%20%7D%204%20x%5E%7B%5Cfrac%7B11%7D%7B10%7D%7D%20%5Ccdot%20y%5E%7B%5Cfrac%7B17%7D%7B3%7D%7D)
.
Answer:
7
Step-by-step explanation:
D a theorem needs to be proven
The answer to this question is the letter "A" which is $20.70. The solution is shown below:
If the guy will solely use the car, his expenses for the gasoline per month is:
Guy alone = $ 2.76/gallon * 15 gallons = $ 41.4
If the guy will let his two officemates ride the car and contribute each quarter of the of a tank:
First officemate = 15/4 * $2.76 = $ 10.35
Second officemate = 15/4 * $2.76 = $10.35
The guy total savings is shown below:
Total savings = $41.4 - $10.35 -$10.35
Total savings = $20.70
The answer is the letter "A".
