1. Integer Exponents Day 2

2. Warm Up Find the value of each power.

3. Explore and apply the properties of integer exponents. Observe patterns to write the general rules of integer exponents. Then use these properties to generate equivalent numerical expressions. Recognize that there are patterns of integer exponents. Make conjectures about the properties of integer exponents. Apply the properties of integer exponents to simplify numerical expressions.

4. To apply the properties of exponents, the bases must be the same. However, some expressions can be manipulated to convert unequal bases. Consider the following examples. Try simplifying each expression by manipulation.

5. To develop the properties of integer exponents, look for patterns in a powers table, in the multiplication and division of powers with the same base, and in powers of products. The properties can be used to simplify complicated expressions.

6. Use your knowledge of the order of operations to help simplify expressions involving exponents by simplifying what you can inside parentheses, and then use the properties of exponents to simplify terms with exponents.

7. (-a) 2 is always positive because the square of any nonzero number is always positive. The order of operations means -a 2 = -( a 2 ), and its value will always be negative.

8. Simplify each expression.

9. To simplify an expression with exponents by applying the properties of exponents the order of operations must always be followed. Each expression within brackets or parentheses must be simplified first. Then terms with the same base that are being multiplied or divided can be simplified using the properties of exponents. Finally, any terms being added or subtracted are simplified.

10. A negative exponent does not mean the answer will be a negative number. When no exponent is given, it is understood that the number is raised to the power of one.

12. The distance from Earth to the moon is about 22 4 miles. The distance from Earth to Neptune is about 22 7 miles. Which distance is the greater distance, and about how many times greater is it?

13. In computer technology, a kilobyte is 2 10 bytes in size. A gigabyte is 2 30 bytes in size. The size of a terabyte is the product of the size of a kilobyte and the size of a gigabyte. What is the size of a terabyte?

14. Exit Ticket