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

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{8 x 5}{8 x 5} \) - \( \frac{4 x 4}{10 x 4} \)

\( \frac{40}{40} \) - \( \frac{16}{40} \)

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

\( \frac{40 - 16}{40} \) = \( \frac{24}{40} \) = \(\frac{3}{5}\)

To simplify a radical, factor out the perfect squares:

\( \sqrt{8} \)
\( \sqrt{4 \times 2} \)
\( \sqrt{2^2 \times 2} \)
2\( \sqrt{2} \)

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:

\( \frac{-4c^6}{9c^2} \)
\( \frac{-4}{9} \) c^{(6 - 2)}
-\(\frac{4}{9}\)c⁴

The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 the greatest factor 32 and 60 have in common.