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:

-1a⁴ - 6a⁴
(-1 - 6)a⁴
-7a⁴

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:

0.0002652 in scientific notation is 2.652 x 10^-4

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 3 crews so there are \( \frac{12}{3} \) = 4 workers on a crew. 8 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 8 x 4 = 32 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 32 - 12 = 20 new staff for the busy season.

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

3\( \sqrt{6} \) x 7\( \sqrt{2} \)
(3 x 7)\( \sqrt{6 \times 2} \)
21\( \sqrt{12} \)

Now we need to simplify the radical:

21\( \sqrt{12} \)
21\( \sqrt{3 \times 4} \)
21\( \sqrt{3 \times 2^2} \)
(21)(2)\( \sqrt{3} \)
42\( \sqrt{3} \)

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

4a³ + 1a³
(4 + 1)a³
5a³