Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (4 + 4) ÷ 4 x 4 - 4²
P: 2 + (8) ÷ 4 x 4 - 4²
E: 2 + 8 ÷ 4 x 4 - 16
MD: 2 + \( \frac{8}{4} \) x 4 - 16
MD: 2 + \( \frac{32}{4} \) - 16
AS: \( \frac{8}{4} \) + \( \frac{32}{4} \) - 16
AS: \( \frac{40}{4} \) - 16
AS: \( \frac{40 - 64}{4} \)
\( \frac{-24}{4} \)
-6

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{64} \) = \( \frac{\frac{40}{8}}{\frac{64}{8}} \) = \( \frac{5}{8} \)

The greatest common factor (GCF) is the greatest factor that divides two integers.

50% of the water consumption is industrial use and 27% is personal use so (50% - 27%) = 23% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{23}{100} \) x 50,000 gallons = 11,500 gallons.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

3y⁶ - 8y⁶
(3 - 8)y⁶
-5y⁶