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:

\( \frac{5y^8}{7y^2} \)
\( \frac{5}{7} \) y^{(8 - 2)}
\(\frac{5}{7}\)y⁶

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:

3c⁵ x 6c⁴
(3 x 6)c^{(5 + 4)}
18c⁹

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

7\( \sqrt{7} \) x 4\( \sqrt{7} \)
(7 x 4)\( \sqrt{7 \times 7} \)
28\( \sqrt{49} \)

Now we need to simplify the radical:

28\( \sqrt{49} \)
28\( \sqrt{7^2} \)
(28)(7)
196

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{6} \) ÷ \( \frac{3}{5} \) = \( \frac{2}{6} \) x \( \frac{5}{3} \)

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

\( \frac{2}{6} \) x \( \frac{5}{3} \) = \( \frac{2 x 5}{6 x 3} \) = \( \frac{10}{18} \) = \(\frac{5}{9}\)

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: