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:

6x⁷ - 7x⁷
(6 - 7)x⁷
-x⁷

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 5}{9 x 5} \) - \( \frac{2 x 3}{15 x 3} \)

\( \frac{20}{45} \) - \( \frac{6}{45} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{20 - 6}{45} \) = \( \frac{14}{45} \) = \(\frac{14}{45}\)

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

If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 29 large cakes are needed for the party so \( \frac{29}{20} \) = 1\(\frac{9}{20}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 11 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 11 x 4 = 44 small cakes during that time. 410 small cakes are needed for the party so \( \frac{410}{44} \) = 9\(\frac{7}{22}\) 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 2 + 10 = 12 cooks.

You have 13 out of the total of 450 raffle tickets sold so you have a (\( \frac{13}{450} \)) x 100 = \( \frac{13 \times 100}{450} \) = \( \frac{1300}{450} \) = 3% chance to win the raffle.