To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{56} \) = \( \frac{\frac{32}{8}}{\frac{56}{8}} \) = \( \frac{4}{7} \)

The greatest common factor (GCF) is the greatest factor that divides two integers.

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. 32 large cakes are needed for the party so \( \frac{32}{4} \) = 8 cooks are needed to bake the required number of large cakes.

If a single cook can bake 12 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 12 x 2 = 24 small cakes during that time. 490 small cakes are needed for the party so \( \frac{490}{24} \) = 20\(\frac{5}{12}\) 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 8 + 21 = 29 cooks.

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:

7z² + 8z²
(7 + 8)z²
15z²

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.