1.1.5 Properties of Exponents and Scientific Notation - Worksheet
Example 1: Write each expression in expanded form. 1. 4( a − b ) 2 2. (12 xy ) 4
3
4. −
d
1 2
3. − s 3 ( − 2 t ) 5
Example 2: Simplify each expression. 5. − 2
3
− 3 5
− 2 3
7.
6. 5 0
8. 10 − 1
Example 3: Simplify each expression. Assume all variables are nonzero. 9. ( − 3 a 2 b 3 ) 2 10. c 3 d 2 ( c − 2 d 4 ) 11. uv u v 5 6 2 2
2
12. 10
5 2
y
x
2
16. − − − x y x y 1 2 3 5
15. b b (4 ) 2
13. − 2 s − 3 t (7 s − 8 t 5 )
14. − 4 m ( mn 2 ) 3
Example 4: Simplify each expression. Write the answer in scientific notation. 17. (2.2 × 10 5 )(4.5 × 10 11 ) 18. × × − 7.8 10 2.6 10 8 3 Example 5: 20. Nanotechnology is a branch of engineering that works with devices that are smaller than 100 nanometers. The width of one string on the playable nanoguitar created by scientists at Cornell University in 2003 is 2.0 × 10 − 7 meters. If the width of a human hair is about 80 microns, how many nanoguitar strings would have the same width as a human hair? ( Hint: 1 micron = 10 − 6 meters)
3 4
× × − 16 10 4.0 10
19.
10 microns
35
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