To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 50mph \times 2h \)
100 miles

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.

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

\( \frac{4}{7} \) ÷ \( \frac{3}{5} \) = \( \frac{4}{7} \) x \( \frac{5}{3} \)

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

\( \frac{4}{7} \) x \( \frac{5}{3} \) = \( \frac{4 x 5}{7 x 3} \) = \( \frac{20}{21} \) = \(\frac{20}{21}\)

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:

2,796,000 in scientific notation is 2.796 x 10⁶