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:

2b⁵ + 5b⁵
(2 + 5)b⁵
7b⁵

You have 21 out of the total of 350 raffle tickets sold so you have a (\( \frac{21}{350} \)) x 100 = \( \frac{21 \times 100}{350} \) = \( \frac{2100}{350} \) = 6% chance to win the raffle.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%

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

\( \frac{7a^7}{4a^2} \)
\( \frac{7}{4} \) a^{(7 - 2)}
1\(\frac{3}{4}\)a⁵

Christine scored 83% on the test meaning she earned 83% of the possible points on the test. There were 90 possible points on the test so she earned 90 x 0.83 = 75 points. Each question is worth 3 points so she got \( \frac{75}{3} \) = 25 questions right.