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

The factors of 64 are [1, 2, 4, 8, 16, 32, 64] and the factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 64 and 40 have in common.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-6x³ - 1x³
(-6 - 1)x³
-7x³

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. 40 large cakes are needed for the party so \( \frac{40}{4} \) = 10 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 2 hours, a single cook can bake 11 x 2 = 22 small cakes during that time. 230 small cakes are needed for the party so \( \frac{230}{22} \) = 10\(\frac{5}{11}\) 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 10 + 11 = 21 cooks.

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

\( \frac{63\sqrt{27}}{9\sqrt{9}} \)
\( \frac{63}{9} \) \( \sqrt{\frac{27}{9}} \)
7 \( \sqrt{3} \)