An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{3a^5}{a^3} \)
\( \frac{3}{1} \) a^{(5 - 3)}
3a²

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

6\( \sqrt{18} \) - 2\( \sqrt{2} \)
6\( \sqrt{9 \times 2} \) - 2\( \sqrt{2} \)
6\( \sqrt{3^2 \times 2} \) - 2\( \sqrt{2} \)
(6)(3)\( \sqrt{2} \) - 2\( \sqrt{2} \)
18\( \sqrt{2} \) - 2\( \sqrt{2} \)

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

The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 16 are [1, 2, 4, 8, 16]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 40 and 16 have in common.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] 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 [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.

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

\( \frac{2 x 2}{4 x 2} \) + \( \frac{5 x 1}{8 x 1} \)

\( \frac{4}{8} \) + \( \frac{5}{8} \)

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

\( \frac{4 + 5}{8} \) = \( \frac{9}{8} \) = 1\(\frac{1}{8}\)