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

9\( \sqrt{8} \) x 3\( \sqrt{7} \)
(9 x 3)\( \sqrt{8 \times 7} \)
27\( \sqrt{56} \)

Now we need to simplify the radical:

27\( \sqrt{56} \)
27\( \sqrt{14 \times 4} \)
27\( \sqrt{14 \times 2^2} \)
(27)(2)\( \sqrt{14} \)
54\( \sqrt{14} \)

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:

0.0004069 in scientific notation is 4.069 x 10^-4

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{64} \) = \( \frac{\frac{28}{4}}{\frac{64}{4}} \) = \( \frac{7}{16} \)

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.