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

3\( \sqrt{9} \) x 5\( \sqrt{6} \)
(3 x 5)\( \sqrt{9 \times 6} \)
15\( \sqrt{54} \)

Now we need to simplify the radical:

15\( \sqrt{54} \)
15\( \sqrt{6 \times 9} \)
15\( \sqrt{6 \times 3^2} \)
(15)(3)\( \sqrt{6} \)
45\( \sqrt{6} \)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

2z⁷ + 1z⁷
(2 + 1)z⁷
3z⁷

1

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

\( \frac{15\sqrt{42}}{3\sqrt{6}} \)
\( \frac{15}{3} \) \( \sqrt{\frac{42}{6}} \)
5 \( \sqrt{7} \)

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).