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

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 54 meters so the equation becomes: 2w + 2h = 54.

Putting these two equations together and solving for width (w):

2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9

Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m²

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

9\( \sqrt{80} \) - 6\( \sqrt{5} \)
9\( \sqrt{16 \times 5} \) - 6\( \sqrt{5} \)
9\( \sqrt{4^2 \times 5} \) - 6\( \sqrt{5} \)
(9)(4)\( \sqrt{5} \) - 6\( \sqrt{5} \)
36\( \sqrt{5} \) - 6\( \sqrt{5} \)

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

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

\( \frac{2}{9} \) ÷ \( \frac{2}{6} \) = \( \frac{2}{9} \) x \( \frac{6}{2} \)

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

\( \frac{2}{9} \) x \( \frac{6}{2} \) = \( \frac{2 x 6}{9 x 2} \) = \( \frac{12}{18} \) = \(\frac{2}{3}\)

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 $300
i = 0.03 x $300

No payments were made so the total amount due is the original amount + the accumulated interest: