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:

0.0005354 in scientific notation is 5.354 x 10^-4

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{2 x 3}{4 x 3} \) + \( \frac{2 x 1}{12 x 1} \)

\( \frac{6}{12} \) + \( \frac{2}{12} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{6 + 2}{12} \) = \( \frac{8}{12} \) = \(\frac{2}{3}\)

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

2\( \sqrt{63} \) - 9\( \sqrt{7} \)
2\( \sqrt{9 \times 7} \) - 9\( \sqrt{7} \)
2\( \sqrt{3^2 \times 7} \) - 9\( \sqrt{7} \)
(2)(3)\( \sqrt{7} \) - 9\( \sqrt{7} \)
6\( \sqrt{7} \) - 9\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{75mi}{15mph} \)
5 hours

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