1. Numerical Expressions Lesson 6.01

2. After completing this lesson, you will be able to say: I can write numerical expressions involving whole-number exponents. I can evaluate numerical expressions involving whole-number exponents. I can solve order of operation expressions that contain exponents.

3. Key Terms Exponential form: A number including a base and an exponent. Base: The number that is multiplied by itself when written in exponential form. Exponent: A number that is written above and to the right of a base to indicate how many times to multiply the base by itself; sometimes called a power

4. Exponential form Exponential form is just a simplified way of writing a multiplication expression where a number is being multiplied by itself

5. Writing a Number in Exponential form

6. Area in Exponential Form Since the 5 is being multiplied by itself 2 times, you can use an exponent of 2. The area 5 ft × 5 ft written in exponential form is 5 2 ft 2. When the exponent is a 2, this is called squaring the base. So you can say "five squared."

7. Volume in Exponential Form To calculate the volume of the circus cube you would multiply 5 ft × 5 ft × 5 ft. 5 is the base, but this time it is multiplied 3 times so the exponent in this case is 3. Therefore, the exponential form of the volume is 5 3 ft 3. When an exponent is a 3, this is called cubing the base. So you can say "five cubed."

8. Example using Exponential Form The goal of this new circus act is for the performers to knock over as many pins as possible. Each pin will knock over three other pins, and each of those will knock over three more pins, and so on. There are five total rows of pins. The expression to see how many pins to knock down in the fifth row is created by multiplying 3 five times. You can write this expression as 3 × 3 × 3 × 3 × 3 or in exponential form as 3 5

9. Try it Ginger, the circus mouse, gave birth to twins. Each of the twins then gave birth to twins. Then those twins gave birth to twins.

10. Check your work To understand how the mice population grew, you would multiply 2 three times. So 2 × 2 × 2 = 2 3 or "two cubed."

11. Reading Exponents An exponent is sometimes referred to as a power. So 5 2 can be read as "five to the power of two." Here are a few other variations for reading exponential expressions: 5252 5353 5454 5 to the second power5 to the third power5 to the fourth power 5 to the power of 25 to the power of 35 to the power of 4 5 squared5 cubed 5 raised to the second power5 raised to the third power5 raised to the fourth power 5 with an exponent of 25 with an exponent of 35 with an exponent of 4

12. Typing Exponents An easy way to represent an exponent is to use the ^ symbol (above the number 6 on your keyboard). So, 5 3 can be typed as 5^3. Example: 64 = 6^4

13. Simplifying exponential numbers 3 5 = 3 x 3 x 3 x 3 x 3 = 3 x 3 x 3 x 3 x 3 9 x 3 x 3 x 3 27 x 3 x 3 81 x 3 243 When simplifying an exponent, you must remember that 7 3 = 7 × 7 × 7. It does not equal 7 × 3 or 7·3 or 73 Caution

14. Try it Simplify the exponential expression of 6.2 4. Be sure to round your answer to the nearest tenths place

15. Check your work 6.2 4 = 6.2 × 6.2 × 6.2 × 6.2 = 1,477.6336 This is 1,477.6 when rounded to the tenths place

16. Evaluating Numerical Expressions When simplifying an expression, you must always follow the order of operations. Order of operations: The rules of which calculation comes first when evaluating an expression

17. Simplifying and Expression Steps to Simplify an expression Step 1: simplify inside parenthesis Step 2: simplify the exponents Step 3: evaluate any multiplication and/or division from left to right Step 4: complete any addition and/or subtraction from left to right

18. Example

19. Try it Simplify the expression 4 3 ÷ (7 − 3) × 2

20. Check your work 4 3 ÷ (7 − 3) × 2 4 3 ÷ 4 × 2 64 ÷ 4 × 2 16 x 2 32

21. Now that you completed this lesson, you should be able to say: I can write numerical expressions involving whole-number exponents. I can evaluate numerical expressions involving whole-number exponents. I can solve order of operation expressions that contain exponents.