To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{4!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{5}{1} \)
5

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

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

\( \frac{2 x 3}{2 x 3} \) - \( \frac{4 x 1}{6 x 1} \)

\( \frac{6}{6} \) - \( \frac{4}{6} \)

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

\( \frac{6 - 4}{6} \) = \( \frac{2}{6} \) = \(\frac{1}{3}\)

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:

\( \frac{-4a^7}{4a^2} \)
\( \frac{-4}{4} \) a^{(7 - 2)}
-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:

\( \sqrt{\frac{49}{36}} \)
\( \frac{\sqrt{49}}{\sqrt{36}} \)
\( \frac{\sqrt{7^2}}{\sqrt{6^2}} \)
\( \frac{7}{6} \)
1\(\frac{1}{6}\)