# Math Problem Sets

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Exercises - Provide calculation steps 1. "Solve the following problems with exponents" Answer: a. 25 =2x2x2x2x2 =4x8 = 32 b. 3-3 = 1/33 =1/3x3x3 =1/9x3 = 1/27 c. 115 = 1x1x1x1x1x1x1x1x1x1x1x1x1x1x1 = 1 d. 02 = 0x0 = 0 e. 223/4 = 4 223 = 4 22x22x22 = 4 10648 = 4 10648 = 10.158 2. "Solve the following problems with roots" Answer: a. 169 = 13x13 = 13 b. 50 = 7.071 x7.071 = 7.071 c. 3 82 (Cube Root of 82) = 3 4.344x4.344x4.344 = 4.344 From the professor Correction to the Module 2 Case Assignment: "Problem 2c. Solve problem with roots: "3[square root symbol]82 (Cube Root of 82)" is inconsistent: "3[square root symbol]82" rather looks like "3 times square root of 82" whereas word representation assumes (82)^(1/3)". 3. "Write the following numbers using powers of 10" Answer a. 10000 = 10x10x10x10 = 101x101x101x101 = 101+1+1+1 = 104 b. 0.0001 = 1/10x10x10x10 = 1/101x101x101x101 = 1/101+1+1+1 =1/104 = 10-4 c. 1 =10/10 =101/101 =10(1-1) = 100 4. "Write the following numbers using scientific notation" Answer a. 5,603 = 5.603 x 1000 = 5.603 x (10x10x10) = 5.603 x 101x101x101 = 5.603 x 101+1+1 = 5.603 x 103 b. 0.000002 = 1/2000, 000 = 1/2 x 1,000,000 = 1/2 x (10x10x10x10x10x10) = 1/2 x (101x101x101x101x101x101) = 1/2 x 101+1+1+1+1+1 = 1/2 x 106 = 2 x 10-6 c. 23 = 2.3 x 10 = 2.3 x 101 5. "Rewrite the following statements using logarithms": Answer a. 4-1=¼ =4-1= 0.25 =log0.25= -1 b.