Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Rewrite each expression using each base only once.

8. 7 3 · 7 4 7 cubed , middle dot , 7 to the fourth
9. ( − 6 ) 12 · ( − 6 ) 5 · ( − 6 ) 2 open negative 6 close to the twelfth . middle dot . open negative 6 close to the fifth . middle dot . open negative 6 close squared
10. 9 6 · 9 − 4 · 9 − 2 9 to the sixth , middle dot , 9 super negative 4 end super , middle dot , 9 super negative 2 end super
11. 2 2 · 2 7 · 2 0 2 squared , middle dot , 2 to the seventh , middle dot , 2 to the
12. 5 − 2 · 5 − 4 · 5 8 5 super negative 2 end super , middle dot , 5 super negative 4 end super , middle dot , 5 to the eighth
13. ( − 8 ) 5 · ( − 8 ) − 5 open negative 8 close to the fifth . middle dot . open negative 8 close super negative 5 end super

See Problem 2.

Simplify each expression.

14. m 3 m 4 m cubed , m to the fourth
15. 5 c 4 · c 6 5 , c to the fourth , middle dot , c to the sixth
16. 4 t − 5 · 2 t − 3 4 , t super negative 5 end super , middle dot 2 , t super negative 3 end super
17. ( 7 x 5 ) ( 8 x ) open 7 , x to the fifth , close open 8 x close
18. 3 x 2 · x 2 3 , x squared , middle dot , x squared
19. ( − 2.4 n 4 ) ( 2 n − 1 ) open negative 2.4 , n to the fourth , close open 2 , n super negative 1 end super , close
20. b − 2 · b 4 · b b super negative 2 end super , middle dot , b to the fourth , middle dot b
21. ( − 2 m 3 ) ( 3.5 m − 3 ) open negative 2 , m cubed , close open 3.5 . m super negative 3 end super , close
22. ( 15 a 3 ) ( − 3 a ) open 15 , eh cubed , close open negative 3 eh close
23. ( x 5 y 2 ) ( x − 6 y ) open , x to the fifth , y squared , close open , x super negative 6 end super , y close
24. ( 5 x 5 ) ( 3 y 6 ) ( 3 x 2 ) open 5 , x to the fifth , close open 3 , y to the sixth , close open 3 , x squared , close
25. ( 4 c 4 ) ( a c 3 ) ( − 3 a 5 c ) open 4 , c to the fourth , close open eh , c cubed , close open negative 3 , eh to the fifth , c close
26. x 6 · y 2 · x 4 x to the sixth , middle dot , y squared , middle dot , x to the fourth
27. a 6 b 3 · a 2 b − 2 eh to the sixth , b cubed , middle dot , eh squared . b super negative 2 end super
28. − m 2 · 4 r 3 · 12 r − 4 · 5 m negative , m squared , middle dot 4 , r cubed , middle dot 12 , r super negative 4 end super , middle dot 5 m

See Problem 3.

Simplify each expression. Write each answer in scientific notation.

29. ( 2 × 10 3 ) ( 3 × 10 2 ) open 2 times , 10 cubed , close open 3 times , 10 squared , close
30. ( 2 × 10 6 ) ( 3 × 10 3 ) open 2 times , 10 to the sixth , close open 3 times , 10 cubed , close
31. ( 4 × 10 6 ) · 10 − 3 open 4 times , 10 to the sixth , close middle dot , 10 super negative 3 end super
32. ( 1 × 10 3 ) ( 3.4 × 10 − 8 ) open 1 times , 10 cubed , close open 3.4 times , 10 super negative 8 end super , close
33. ( 8 × 10 − 5 ) ( 7 × 10 − 3 ) open 8 times , 10 super negative 5 end super , close open 7 times , 10 super negative 3 end super , close
34. ( 5 × 10 7 ) ( 3 × 10 14 ) open 5 times , 10 to the seventh , close open 3 times , 10 to the fourteenth , close

See Problem 4.

Write each answer in scientific notation.

35. Astronomy The distance light travels in one second (one light-second) is about 1.86 × 10 5 1.86 , times , 10 to the fifth  mi. Saturn is about 475 light-seconds from the sun. About how many miles from the sun is Saturn?
36. Biology A human body contains about 2.7 × 10 4 2.7 times , 10 to the fourth  microliters (μL) of blood for each pound of body weight. Each microliter of blood contains about 7 × 10 4 7 times , 10 to the fourth  white blood cells. About how many white blood cells are in the body of a 140-lb person?

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