To subtract these radicals together their radicands must be the same:

5\( \sqrt{18} \) - 7\( \sqrt{2} \)
5\( \sqrt{9 \times 2} \) - 7\( \sqrt{2} \)
5\( \sqrt{3^2 \times 2} \) - 7\( \sqrt{2} \)
(5)(3)\( \sqrt{2} \) - 7\( \sqrt{2} \)
15\( \sqrt{2} \) - 7\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

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:

-8b⁶ - 4b⁶
(-8 - 4)b⁶
-12b⁶

There are 3 5-passenger taxis available so that's 3 x 5 = 15 total seats. There are 20 people needing transportation leaving 20 - 15 = 5 who will have to find other transportation.

If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 21 large cakes are needed for the party so \( \frac{21}{9} \) = 2\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 18 x 3 = 54 small cakes during that time. 320 small cakes are needed for the party so \( \frac{320}{54} \) = 5\(\frac{25}{27}\) 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 3 + 6 = 9 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).