The amount of flour you need is (3\(\frac{5}{8}\) - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{29}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{23}{8} \) cups
2\(\frac{7}{8}\) cups

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 have in common.

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:

9,780,000 in scientific notation is 9.78 x 10⁶

First, solve for \( \left|x - 3\right| \):

\( \left|x - 3\right| \) - 7 = 3
\( \left|x - 3\right| \) = 3 + 7
\( \left|x - 3\right| \) = 10

The value inside the absolute value brackets can be either positive or negative so (x - 3) must equal + 10 or -10 for \( \left|x - 3\right| \) to equal 10:

So, x = -7 or x = 13.

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:

-9z² x 3z⁶
(-9 x 3)z^{(2 + 6)}
-27z⁸