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).

To simplify a radical, factor out the perfect squares:

\( \sqrt{8} \)
\( \sqrt{4 \times 2} \)
\( \sqrt{2^2 \times 2} \)
2\( \sqrt{2} \)

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

2 + (3 + 2) ÷ 4 x 3 - 2²
P: 2 + (5) ÷ 4 x 3 - 2²
E: 2 + 5 ÷ 4 x 3 - 4
MD: 2 + \( \frac{5}{4} \) x 3 - 4
MD: 2 + \( \frac{15}{4} \) - 4
AS: \( \frac{8}{4} \) + \( \frac{15}{4} \) - 4
AS: \( \frac{23}{4} \) - 4
AS: \( \frac{23 - 16}{4} \)
\( \frac{7}{4} \)
1\(\frac{3}{4}\)

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{18\sqrt{24}}{6\sqrt{8}} \)
\( \frac{18}{6} \) \( \sqrt{\frac{24}{8}} \)
3 \( \sqrt{3} \)

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.