To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-6y⁴ x 2y⁶
(-6 x 2)y^{(4 + 6)}
-12y¹⁰

25% of the water consumption is industrial use and 10% is personal use so (25% - 10%) = 15% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{15}{100} \) x 30,000 gallons = 4,500 gallons.

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 50.4km + 3.4000000000000004km
total distance = 53.9km

If 48% of the town's 47,000 voters cast ballots the number of votes cast is:

(\( \frac{48}{100} \)) x 47,000 = \( \frac{2,256,000}{100} \) = 22,560

The mayor got 56% of the votes cast which is:

(\( \frac{56}{100} \)) x 22,560 = \( \frac{1,263,360}{100} \) = 12,634 votes.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.