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 these radicals together their radicands must be the same:

6\( \sqrt{175} \) + 5\( \sqrt{7} \)
6\( \sqrt{25 \times 7} \) + 5\( \sqrt{7} \)
6\( \sqrt{5^2 \times 7} \) + 5\( \sqrt{7} \)
(6)(5)\( \sqrt{7} \) + 5\( \sqrt{7} \)
30\( \sqrt{7} \) + 5\( \sqrt{7} \)

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

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%

To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{44} \) = \( \frac{\frac{24}{4}}{\frac{44}{4}} \) = \( \frac{6}{11} \)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: