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.

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:

9y⁶ + 7y⁶
(9 + 7)y⁶
16y⁶

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 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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

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

Now that the radicands are identical, you can add them together: