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

4\( \sqrt{6} \) x 9\( \sqrt{7} \)
(4 x 9)\( \sqrt{6 \times 7} \)
36\( \sqrt{42} \)

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

7\( \sqrt{63} \) - 4\( \sqrt{7} \)
7\( \sqrt{9 \times 7} \) - 4\( \sqrt{7} \)
7\( \sqrt{3^2 \times 7} \) - 4\( \sqrt{7} \)
(7)(3)\( \sqrt{7} \) - 4\( \sqrt{7} \)
21\( \sqrt{7} \) - 4\( \sqrt{7} \)

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

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{9} \) x \( \frac{1}{7} \) = \( \frac{1 x 1}{9 x 7} \) = \( \frac{1}{63} \) = \(\frac{1}{63}\)

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:

\( \frac{3b^5}{7b^3} \)
\( \frac{3}{7} \) b^{(5 - 3)}
\(\frac{3}{7}\)b²