A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

6,167,000 in scientific notation is 6.167 x 10⁶

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

\( \frac{12\sqrt{8}}{6\sqrt{4}} \)
\( \frac{12}{6} \) \( \sqrt{\frac{8}{4}} \)
2 \( \sqrt{2} \)

To add 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:

\( \frac{9 x 3}{2 x 3} \) + \( \frac{5 x 1}{6 x 1} \)

\( \frac{27}{6} \) + \( \frac{5}{6} \)

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

\( \frac{27 + 5}{6} \) = \( \frac{32}{6} \) = 5\(\frac{1}{3}\)

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:

\( \frac{-7x^6}{3x^2} \)
\( \frac{-7}{3} \) x^{(6 - 2)}
-2\(\frac{1}{3}\)x⁴

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

8c³ - 3c³
(8 - 3)c³
5c³