Activities

1. Simplify the expression (4a²b³c⁴)².

2. Simplify the expression (3m²n²m)^-1.

3. Evaluate the expression (3x)^-2 when x = -4.

4. Simplify the expression .

5. Simplify the expression .

6. Simplify the expression

7. Evaluate the expression |x^-1 – 4| when x equals 2.

8. Given the expression determine the equivalent expression when m=2 and when m =-2.

9. Determine values for a, b, and c so that = 0.25.

10. Simplify the following expression: |(3(x³)²)(-2x⁴)(5(x^-3)⁵)|

11. Describe in your own words, and using examples, why and (3^x)^y = 3^z.

12. What value does equal when b is two?

13. Simplify the following expression:  .

14. The expression 2(3²x⁴y⁵z)^a is equivalent to 1458x¹²y¹⁵z³ for what value of a?

15. Represent the equation using the form , where x, y, z, and w are integers.

16. Determine the values for a, b, c, and d so that   simplifies to the expression .

17. A rectangular prism has a length of 3x³y inches and a width of 2x^-1y⁴ inches and a height of 5x²y^-2. What is the surface area of the table in terms of x and y?

18. Ms. Julia knows that the area of one floor tile in her classroom can be represented by the expression   inches per tile. If her classroom has a width of 28 tiles and a length of 40 tiles, then what is the area of her classroom in square feet?

Answer Key/Rubric

1. 16a⁴b⁶c⁸

3.   or 

4. .

7. 3.5
8. When m = 2 the expression is 4a⁴b⁶, when m = -2 the expression is

9. Various answers including a=2, b=3 and c = 7 (Reason: After simplifying you have 2^{a + b – c} = 0.25 so a+b-c must equal -2)

11. Various answers including. and

12. 1

13. x⁴

14. a = 3

15. x = 10, y = 4, z = 7, and w = -1

16. a = 4, b = 5, c = -2, and d = 8

18. 11,468.8  square feet