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Name: ________________________ Class: _________________ Bases and Exponents Practice II o I can solve problems involving powers o I can explain and apply all of the exponent laws o I can use the order of operations on expressions with powers 1. Write each expression as a single power and then evaluate. a) 6 4 6 3 b) (11) 7 (11) 5 c) 3 4 35 33 d) 56 53 5 e) (4) 3 (4) 6 (4) 2 (4) 4 f) 10 6 10 0 10 3 10 2 2. Why do you add the exponents to simplify the expression 3 2 3 4 but multiplying the exponent to simplify the expression (32 ) 4 ? 3. Write each expression as a product of powers: Expression a) (6 4) 3 Product of Powers Expression b) (2 5) 4 c) {( 2) 3)}5 d) (25 4) 2 e) (11 3)1 f) {( 3) (4)}3 4. Write each expression as a single power: Product of Powers Name: ________________________ Class: _________________ Expression a) (32 ) 4 Single Power Expression b) (6 3 ) 3 c) (5 3 )1 d) (7 6 ) 0 e) (8 2 ) 2 f) {(3) 4 }2 5. Simplify each expression. Then evaluate. a) (2 2 ) 4 b) - (33 ) 3 c) {(5) 2 }3 d) (9 4) 2 e) {( 2) 3)}3 f) - (3 4) 2 6. Evaluate: a) 3 4 3 2 c) 10 3 10 2 7. Simplify each expression. Then evaluate. b) (4) 2 (4) 3 d) (5) 4 (5) 2 Single Power Name: ________________________ Class: _________________ a) (32 31 ) 2 b) (4 6 4 4 ) 2 c) (12 2 ) 4 (12 3 ) 2 d) {( 2) 0 (2) 3 }2 e) (10 6 10 4 ) 3 f) 8. Simplify each expression. Then evaluate. a) 3 2 3 8 4 (5 2 ) 6 (53 ) 4 b) (2 3 ) 4 (2 4 2 3 ) 2 c) (4 2) 4 (53 ) 2 d) 2 3 (5 2) 4 e) (23 2 6 ) 2 (37 35 ) 4 f) {( 4) 3 (4) 2 }2 (4 2 ) 2 Name: ________________________ Class: _________________ 9. An alfalfa field is a rectangle, 10 4 m long and 10 3 wide. Write an expression for the area of the alfalfa field. Then evaluate. 10. A type of bacteria is known to double every hour. There are 50 bacteria to start with. How many will there be after: a) 3 hours b) 9 hours c) 15 hours 11. A standard combination lock has 40 numbers on its face from 0 to 39. A combination consists of three numbers, and numbers can be repeated. What is the total number of possible combinations? Express as a power and then evaluate. 12. A white square with a side length of 8 cm is placed on a black square with a side length of 10 cm. a) Write an expression with powers to determine the visible black area. b) What is the visible black area?