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:

1,957,000 in scientific notation is 1.957 x 10⁶

To subtract 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:

\( \frac{3 x 3}{4 x 3} \) - \( \frac{8 x 1}{12 x 1} \)

\( \frac{9}{12} \) - \( \frac{8}{12} \)

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

\( \frac{9 - 8}{12} \) = \( \frac{1}{12} \) = \(\frac{1}{12}\)

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{66}{6} \) = 11

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:

5z² x 9z⁴
(5 x 9)z^{(2 + 4)}
45z⁶

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{81}{81}} \)
\( \frac{\sqrt{81}}{\sqrt{81}} \)
\( \frac{\sqrt{9^2}}{\sqrt{9^2}} \)
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