The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{64}} \)
\( \frac{\sqrt{49}}{\sqrt{64}} \)
\( \frac{\sqrt{7^2}}{\sqrt{8^2}} \)
\(\frac{7}{8}\)

If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 33 large cakes are needed for the party so \( \frac{33}{20} \) = 1\(\frac{13}{20}\) 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. 340 small cakes are needed for the party so \( \frac{340}{44} \) = 7\(\frac{8}{11}\) 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 2 + 8 = 10 cooks.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

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:

\( \frac{-8b^6}{5b^4} \)
\( \frac{-8}{5} \) b^{(6 - 4)}
-1\(\frac{3}{5}\)b²