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

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{14 + 6 + 12 + 8}{4} \) = \( \frac{40}{4} \) = 10

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. 38 large cakes are needed for the party so \( \frac{38}{6} \) = 6\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 17 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 17 x 2 = 34 small cakes during that time. 110 small cakes are needed for the party so \( \frac{110}{34} \) = 3\(\frac{4}{17}\) 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 7 + 4 = 11 cooks.

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 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{60} \) = \( \frac{\frac{32}{4}}{\frac{60}{4}} \) = \( \frac{8}{15} \)

To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{49\sqrt{27}}{7\sqrt{9}} \)
\( \frac{49}{7} \) \( \sqrt{\frac{27}{9}} \)
7 \( \sqrt{3} \)