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:

7x² + 7x²
(7 + 7)x²
14x²

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

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:

\( \frac{3c^6}{8c^4} \)
\( \frac{3}{8} \) c^{(6 - 4)}
\(\frac{3}{8}\)c²

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 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%