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

2\( \sqrt{3} \) x 8\( \sqrt{8} \)
(2 x 8)\( \sqrt{3 \times 8} \)
16\( \sqrt{24} \)

Now we need to simplify the radical:

16\( \sqrt{24} \)
16\( \sqrt{6 \times 4} \)
16\( \sqrt{6 \times 2^2} \)
(16)(2)\( \sqrt{6} \)
32\( \sqrt{6} \)

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

47,000 fans x \( \frac{3}{4} \) = \( \frac{141000}{4} \) = 35,250 fans.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{30mi}{30mph} \)
1 hour

The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.

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