54% of the water consumption is industrial use and 35% is personal use so (54% - 35%) = 19% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{19}{100} \) x 10,000 gallons = 1,900 gallons.

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:

6y³ x 6y⁵
(6 x 6)y^{(3 + 5)}
36y⁸

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

5 + (2 + 5) ÷ 3 x 2 - 3²
P: 5 + (7) ÷ 3 x 2 - 3²
E: 5 + 7 ÷ 3 x 2 - 9
MD: 5 + \( \frac{7}{3} \) x 2 - 9
MD: 5 + \( \frac{14}{3} \) - 9
AS: \( \frac{15}{3} \) + \( \frac{14}{3} \) - 9
AS: \( \frac{29}{3} \) - 9
AS: \( \frac{29 - 27}{3} \)
\( \frac{2}{3} \)
\(\frac{2}{3}\)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{81}} \)
\( \frac{\sqrt{16}}{\sqrt{81}} \)
\( \frac{\sqrt{4^2}}{\sqrt{9^2}} \)
\(\frac{4}{9}\)

To subtract these radicals together their radicands must be the same:

6\( \sqrt{63} \) - 9\( \sqrt{7} \)
6\( \sqrt{9 \times 7} \) - 9\( \sqrt{7} \)
6\( \sqrt{3^2 \times 7} \) - 9\( \sqrt{7} \)
(6)(3)\( \sqrt{7} \) - 9\( \sqrt{7} \)
18\( \sqrt{7} \) - 9\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them: