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

4\( \sqrt{63} \) + 4\( \sqrt{7} \)
4\( \sqrt{9 \times 7} \) + 4\( \sqrt{7} \)
4\( \sqrt{3^2 \times 7} \) + 4\( \sqrt{7} \)
(4)(3)\( \sqrt{7} \) + 4\( \sqrt{7} \)
12\( \sqrt{7} \) + 4\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

First, solve for \( \left|y - 1\right| \):

\( \left|y - 1\right| \) - 4 = -9
\( \left|y - 1\right| \) = -9 + 4
\( \left|y - 1\right| \) = -5

The value inside the absolute value brackets can be either positive or negative so (y - 1) must equal - 5 or --5 for \( \left|y - 1\right| \) to equal -5:

So, y = 6 or y = -4.

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

8x² x 6x⁶
(8 x 6)x^{(2 + 6)}
48x⁸

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 divide fractions, invert the second fraction and then multiply:

\( \frac{4}{7} \) ÷ \( \frac{1}{5} \) = \( \frac{4}{7} \) x \( \frac{5}{1} \)

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

\( \frac{4}{7} \) x \( \frac{5}{1} \) = \( \frac{4 x 5}{7 x 1} \) = \( \frac{20}{7} \) = 2\(\frac{6}{7}\)