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:

0.0008473 in scientific notation is 8.473 x 10^-4

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{7z^7}{4z^3} \)
\( \frac{7}{4} \) z^{(7 - 3)}
1\(\frac{3}{4}\)z⁴

If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 36 large cakes are needed for the party so \( \frac{36}{6} \) = 6 cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 18 x 2 = 36 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{36} \) = 13\(\frac{1}{18}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 6 + 14 = 20 cooks.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{6!} \)
\( \frac{3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4} \)
\( \frac{1}{120} \)

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

2y⁴ + 7y⁴
(2 + 7)y⁴
9y⁴