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:

\( \frac{-3z^7}{7z^4} \)
\( \frac{-3}{7} \) z^{(7 - 4)}
-\(\frac{3}{7}\)z³

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

8\( \sqrt{3} \) x 7\( \sqrt{5} \)
(8 x 7)\( \sqrt{3 \times 5} \)
56\( \sqrt{15} \)

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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

7\( \sqrt{175} \) + 3\( \sqrt{7} \)
7\( \sqrt{25 \times 7} \) + 3\( \sqrt{7} \)
7\( \sqrt{5^2 \times 7} \) + 3\( \sqrt{7} \)
(7)(5)\( \sqrt{7} \) + 3\( \sqrt{7} \)
35\( \sqrt{7} \) + 3\( \sqrt{7} \)

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

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (5 + 2) ÷ 5 x 2 - 3²
P: 5 + (7) ÷ 5 x 2 - 3²
E: 5 + 7 ÷ 5 x 2 - 9
MD: 5 + \( \frac{7}{5} \) x 2 - 9
MD: 5 + \( \frac{14}{5} \) - 9
AS: \( \frac{25}{5} \) + \( \frac{14}{5} \) - 9
AS: \( \frac{39}{5} \) - 9
AS: \( \frac{39 - 45}{5} \)
\( \frac{-6}{5} \)
-1\(\frac{1}{5}\)