Download ~ Section 7.3 ~ Multiplication Properties of Exponents Packet and more Schemes and Mind Maps Pre-Calculus in PDF only on Docsity!
~ Section 7.3 ~ Multiplication
Properties of Exponents Packet
Warm ups… Write each expression using an exponent.
- 2 2 2 2. x x x x 3. 3 3 x x x y y y y
Write each expression without using an exponent. (expand the expression, do not simplify)
- 43 5. x y^5 3 6. 73 a b^6
You have seen that exponential expressions are useful when writing very small or very large numbers. To perform operations on these numbers, you can use properties of exponents. You can also use these properties to simplify your answer. In this lesson, you will learn some properties that will help you simplify exponential expressions containing multiplication.
n a
The number a is the __________, and the number n is the ______________________. The expression an is called a power and is read “ a to the n th power.”
TLW be able to use the multiplication properties of exponents with variables of the same base
TLW think ‘whoa check out that hoodie model… wonder if I could be a hoodie model too’
TLW use multiplication properties of exponents to evaluate and simplify expressions.
Let’s try some examples… Simplify each expression using the product of powers property. Do not evaluate numbers raised to a ridiculous power.
- 24 34 2 ^2 32 2. q^3^ r^2 q^6 3. n^3^ n ^4 n
- 78 74 5. 3 ^3 58 34 52 6. n m n^4 ^5
GUIDED PRACTICE Simplify each expression using the swell new properties of exponents you just learned.
- c^4 c^3^ c^2 2. x^12^ x^32 y^5 3. 32 31 4. 4 2 43
5. 3 m 5^ 2 m^3 6. 2 x 3 x^3 5 x ^2 7. 2 a b^2 3^ 5 ab^4 8.
7 11 x
9. 2 xy^9^ 4 x y z^2 4 3 10.
2 4 0
5 s t 11. 10 2 109 12.
4 5 5
3 2
2 x 14. 5 a ^2 15. 16 2 ^2 16.
2 3 x x 3 x
17. 3 a 2 1 a ^4 18.
30 0 5, 438,111 x 19. (^) 2 xy (^) (^3) x^2 20. 2 2 ab a b
Name: ____________________________________ Date: ___________________ Period: _______ Multiplication Exponents WS (1) Math is Exponentially Awesome Simplify each expression using properties of exponents. Evaluate where appropriate.
1.^ x x ____________ 2. y y^2 ____________ 3. n^5 n^7 ____________
4. n n^3 ____________ 5. x^5^ x^19 ____________ 6.
2 3 4 x x ____________
9 3 y ____________ 8. (^) n^2 n ^4 ____________ 9. y^3 y^4 ____________
82 7 y ____________ 11. (^) 2 x (^) ^2 y^3 ____________ 12. (^) 7 xy (^) ^2 5 x^2 ____________
- 2 3 xy ^3 ____________ 14. m n m n^2 7 3 ^5 ____________ 15. (^) 4 xy ^2 ____________
16. ^2 ^4 rt ^2 ____________ 17. 2 m n^5 8 8 mn ____________ 18. y^ ^2 y ^3 ____________
*19. 3 ab 3 ab^2^ 3 a b^2 2 ____________ *20.^1 4 3 ^3 42,501, 222^0
(^) xy ____________
Name: ____________________________________ Date: ___________________ Period: _______ Multiplication Exponents WS (3) Math is Heroic Simplify each expression using properties of exponents. Evaluate where appropriate.
2 32 x 4 x _______________ 2. 4 x^2 4 x ^2 _______________
3. 8 ab^2 ^2 _______________ 4.^1 2 6 4 ^2
(^) n n
5. 5 x^12^ 2 x^3 ^3 _______________ 6. a b^2 ^4 _______________
- (^) y^4^ y ^3 y^2 _______________ 8. 101 103 _______________
a^ ^ ab
_______________ 10. ( 9 x y^3 2 )^2 _______________
2 4
3 ab c _______________ 12. 6 m n^3^7 4 m n^2 ^5 _______________
- (^) 10 xy (^) ^2 3 x^2 _______________ 14. (^506) 506$!& %^0 _______________
2 2 22
2 tw 5 tw _______________ 16. 436 !@#$% & ^0 _______________
Name: _____________________________________ Date: ______________________ Period: _________ Exponents M & N Review SIMPLIFY AND REWRITE THE FOLLOWING EXPRESSIONS USING POSITIVE EXPONENTS ONLY.
- 6 x^6^ x^9 1. _____________
8 4 2 x 2. _____________
- 3 x ^4 3. _____________
5 3 5 x 4. _____________
- 7 x^10^ 9 x^9 5. _____________
6. 6 x ^3 ^4 6. _____________
3 2 7 x 7. _____________
2 (^410) 5
(^) x
6 2 5 x 9. _____________
3 5 2 x y 10. _____________
Exponents Super Quiz Review SIMPLIFY AND REWRITE THE FOLLOWING EXPRESSIONS USING POSITIVE EXPONENTS ONLY.
- x^12^ x^8 1. _______________
22 3 x 2. _______________
2 2 11 x 3. _______________
4. 3 x y^5 8 ^2 4. _______________
- (^) 5 x (^) ^3 x ^2 5. _______________
6. xy^20 ^8 z ^4 6. _______________
11 4 3 x 2 y 7. _______________
8. 10 x^27 7 x^3 8. _______________
- (^) 15 x (^) ^2 6 y^25 9. _______________
8 4 x
- ( 12 ab^3 )^2 11. _______________
