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:

8c⁴ x 3c²
(8 x 3)c^{(4 + 2)}
24c⁶

To fill a 12 gallon tank exactly halfway you'll need 6 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{6 \text{ gallons}}{2 \text{ gallons}} \) = 3

If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 27 large cakes are needed for the party so \( \frac{27}{12} \) = 2\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 11 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 11 x 4 = 44 small cakes during that time. 150 small cakes are needed for the party so \( \frac{150}{44} \) = 3\(\frac{9}{22}\) 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 3 + 4 = 7 cooks.

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

\( \left|z - 3\right| \) - 4 = 4
\( \left|z - 3\right| \) = 4 + 4
\( \left|z - 3\right| \) = 8

The value inside the absolute value brackets can be either positive or negative so (z - 3) must equal + 8 or -8 for \( \left|z - 3\right| \) to equal 8:

So, z = -5 or z = 11.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.