To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{68} \) = \( \frac{\frac{20}{4}}{\frac{68}{4}} \) = \( \frac{5}{17} \)

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $400
i = 0.02 x $400
i = $8

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:

5\( \sqrt{45} \) + 3\( \sqrt{5} \)
5\( \sqrt{9 \times 5} \) + 3\( \sqrt{5} \)
5\( \sqrt{3^2 \times 5} \) + 3\( \sqrt{5} \)
(5)(3)\( \sqrt{5} \) + 3\( \sqrt{5} \)
15\( \sqrt{5} \) + 3\( \sqrt{5} \)

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

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:

-4a⁷ x 8a⁷
(-4 x 8)a^{(7 + 7)}
-32a¹⁴