A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (3 + 3) ÷ 4 x 4 - 2²
P: 2 + (6) ÷ 4 x 4 - 2²
E: 2 + 6 ÷ 4 x 4 - 4
MD: 2 + \( \frac{6}{4} \) x 4 - 4
MD: 2 + \( \frac{24}{4} \) - 4
AS: \( \frac{8}{4} \) + \( \frac{24}{4} \) - 4
AS: \( \frac{32}{4} \) - 4
AS: \( \frac{32 - 16}{4} \)
\( \frac{16}{4} \)
4

1

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{2 x 4}{6 x 4} \) - \( \frac{2 x 3}{8 x 3} \)

\( \frac{8}{24} \) - \( \frac{6}{24} \)

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

\( \frac{8 - 6}{24} \) = \( \frac{2}{24} \) = \(\frac{1}{12}\)

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 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%