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:

\( \frac{4a^8}{5a^3} \)
\( \frac{4}{5} \) a^{(8 - 3)}
\(\frac{4}{5}\)a⁵

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{25}{4}} \)
\( \frac{\sqrt{25}}{\sqrt{4}} \)
\( \frac{\sqrt{5^2}}{\sqrt{2^2}} \)
\( \frac{5}{2} \)
2\(\frac{1}{2}\)

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

7\( \sqrt{125} \) - 3\( \sqrt{5} \)
7\( \sqrt{25 \times 5} \) - 3\( \sqrt{5} \)
7\( \sqrt{5^2 \times 5} \) - 3\( \sqrt{5} \)
(7)(5)\( \sqrt{5} \) - 3\( \sqrt{5} \)
35\( \sqrt{5} \) - 3\( \sqrt{5} \)

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

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{18 + 12 + 19 + 11}{4} \) = \( \frac{60}{4} \) = 15

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