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:

1x³ + 3x³
(1 + 3)x³
4x³

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:

0.000408 in scientific notation is 4.08 x 10^-4

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

2x² x 8x⁷
(2 x 8)x^{(2 + 7)}
16x⁹

To add these radicals together their radicands must be the same:

7\( \sqrt{27} \) + 2\( \sqrt{3} \)
7\( \sqrt{9 \times 3} \) + 2\( \sqrt{3} \)
7\( \sqrt{3^2 \times 3} \) + 2\( \sqrt{3} \)
(7)(3)\( \sqrt{3} \) + 2\( \sqrt{3} \)
21\( \sqrt{3} \) + 2\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

To simplify a radical, factor out the perfect squares:

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