To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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:

\( \frac{8y^6}{y^3} \)
\( \frac{8}{1} \) y^{(6 - 3)}
8y³

If a single cook can bake 4 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 4 x 2 = 8 large cakes during that time. 35 large cakes are needed for the party so \( \frac{35}{8} \) = 4\(\frac{3}{8}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 16 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 16 x 2 = 32 small cakes during that time. 420 small cakes are needed for the party so \( \frac{420}{32} \) = 13\(\frac{1}{8}\) 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 5 + 14 = 19 cooks.

To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{24}{68} \) = \( \frac{\frac{24}{4}}{\frac{68}{4}} \) = \( \frac{6}{17} \)