A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

To divide fractions, invert the second fraction and then multiply:

\( \frac{1}{5} \) ÷ \( \frac{4}{5} \) = \( \frac{1}{5} \) x \( \frac{5}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{5} \) x \( \frac{5}{4} \) = \( \frac{1 x 5}{5 x 4} \) = \( \frac{5}{20} \) = \(\frac{1}{4}\)

To simplify a radical, factor out the perfect squares:

\( \sqrt{32} \)
\( \sqrt{16 \times 2} \)
\( \sqrt{4^2 \times 2} \)
4\( \sqrt{2} \)

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

6\( \sqrt{75} \) + 9\( \sqrt{3} \)
6\( \sqrt{25 \times 3} \) + 9\( \sqrt{3} \)
6\( \sqrt{5^2 \times 3} \) + 9\( \sqrt{3} \)
(6)(5)\( \sqrt{3} \) + 9\( \sqrt{3} \)
30\( \sqrt{3} \) + 9\( \sqrt{3} \)

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

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:

0.0000446 in scientific notation is 4.46 x 10^-5