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

\( \frac{10\sqrt{12}}{5\sqrt{3}} \)
\( \frac{10}{5} \) \( \sqrt{\frac{12}{3}} \)
2 \( \sqrt{4} \)

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 18 meters so the equation becomes: 2w + 2h = 18.

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

2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h

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

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

Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m²

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

The factors of a number are all positive integers that divide evenly into the number. The factors of 64 are 1, 2, 4, 8, 16, 32, 64.

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 2}{4 x 2} \) - \( \frac{4 x 1}{8 x 1} \)

\( \frac{14}{8} \) - \( \frac{4}{8} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{14 - 4}{8} \) = \( \frac{10}{8} \) = 1\(\frac{1}{4}\)