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).

The factors of a number are all positive integers that divide evenly into the number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 4h \)
100 miles

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

7\( \sqrt{112} \) - 9\( \sqrt{7} \)
7\( \sqrt{16 \times 7} \) - 9\( \sqrt{7} \)
7\( \sqrt{4^2 \times 7} \) - 9\( \sqrt{7} \)
(7)(4)\( \sqrt{7} \) - 9\( \sqrt{7} \)
28\( \sqrt{7} \) - 9\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.

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

\( \frac{6 x 3}{3 x 3} \) - \( \frac{9 x 1}{9 x 1} \)

\( \frac{18}{9} \) - \( \frac{9}{9} \)

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

\( \frac{18 - 9}{9} \) = \( \frac{9}{9} \) = 1