The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 have in common.

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

-9x⁶ + 1x⁶
(-9 + 1)x⁶
-8x⁶

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 31 large cakes are needed for the party so \( \frac{31}{10} \) = 3\(\frac{1}{10}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 14 x 2 = 28 small cakes during that time. 220 small cakes are needed for the party so \( \frac{220}{28} \) = 7\(\frac{6}{7}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 8 = 12 cooks.

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

36,000 fans x \( \frac{3}{4} \) = \( \frac{108000}{4} \) = 27,000 fans.

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

5\( \sqrt{45} \) - 9\( \sqrt{5} \)
5\( \sqrt{9 \times 5} \) - 9\( \sqrt{5} \)
5\( \sqrt{3^2 \times 5} \) - 9\( \sqrt{5} \)
(5)(3)\( \sqrt{5} \) - 9\( \sqrt{5} \)
15\( \sqrt{5} \) - 9\( \sqrt{5} \)

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