An exponential expression consists of a base and a power. The general format of an exponential expression is bn, where b is the base and n is the power or exponent. The base, b, has to be a positive number, and the power, n, is a real number. Positive powers, negative powers, and fractional powers all have special meanings and designations.
Here are some of the things you do in this chapter:
Be sure you also remember the following:
141–150 Perform the operations and simplify.
141. 32 · 33
142. 2−1 · 26
143. 4 · 42 · 4−1
144. 5 · 5−3 · 55
145.
146.
147.
148.
149.
150.
151–160 Compute the powers and simplify your answers.
151. (22)3
152. (32)2
153. (44)1/2
154. (31/3)6
155. (5−2)−1
157. (39)−1/3
158. (4−2/5)−10
159. (5−2/7)7
160. (6−4/3)−3/4
161–170 Use the order of operations to compute the final answers.
161.
162.
163. 4−3(42)2
164. (5−1)3 (54)1/2
165. (6−3)−1 (62)−2
166. 43 ÷ (48)3/4
167. (2−3)−4 ÷ (23)2 (24)1/4
168. (42)−1/2 (23)2
169. (61/2)4 ÷ (4−1/2)−2
170. (22)3 (23)2 ÷ (22)2 (23)3
171–180 Perform the operations by changing the numbers to the same base.
171. 24 · 4−1
172. 3−2 · 272
173. 41/3 · 82 · 24/3
174. 53 · 25−2
175. (4−3)2 (81/3)
176. (92)−1 (27)3
177. 61/3 · 22/3 · 3−4/3
178. 12−1 · 32 · 4
179. 321/2(83)1/2
180. 49−1/3(72)−1/6
181–190 Perform the operations on the numbers written in scientific notation. Write your answer in scientific notation.
181. (2 × 102)(4 × 104)
182. (3 × 104)(1.7 × 10−2)
183. (6 × 103)(8 × 107)
184. (5 × 10−3)(9 × 10−4)
185. (6.4 × 1010)(5.2 × 10−10)
186. (9 × 10−2) ÷ (3 × 10−4)
187. (1.8 × 104) ÷ (3.6 × 10−2)
188. (5.1 × 10−2) ÷ (3 × 10−2)
189. (1.44 × 105) ÷ (1.6 × 10−7)
190. (1 × 10−17) ÷ (8 × 10−15)
3.142.98.108