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:

5,226,000 in scientific notation is 5.226 x 10⁶

If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 34 large cakes are needed for the party so \( \frac{34}{4} \) = 8\(\frac{1}{2}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 13 x 2 = 26 small cakes during that time. 350 small cakes are needed for the party so \( \frac{350}{26} \) = 13\(\frac{6}{13}\) 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 9 + 14 = 23 cooks.

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

\( \frac{2}{5} \) ÷ \( \frac{1}{8} \) = \( \frac{2}{5} \) x \( \frac{8}{1} \)

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

\( \frac{2}{5} \) x \( \frac{8}{1} \) = \( \frac{2 x 8}{5 x 1} \) = \( \frac{16}{5} \) = 3\(\frac{1}{5}\)

To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{7\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 5

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:

-3x⁴ + 4x⁴
(-3 + 4)x⁴
x⁴