Zero and Negative Exponents
 GOAL: I can simplify exponent expressions that contain zero and negative exponents

 Learning Standards Common Core Standard: 7.EE.1

 Resources RED BOOK Reference: Pages: 417 ─ 421  Practice on page 421,#23-37 odds. BLACK BOOK Reference: Pages: 414 ─ 417  Practice on page 417,#9-35 odds.

 Practices (with answers) Zero and Negative Exponents (ver. 3)

 Lesson Vocabulary Exponent A number written above and to the right of another number, variable, or mathematical expression that shows how many times the number, variable, or expression is multiplied by itself.

 Video Tutorials Topic Description Time (min: sec) Exponent Properties 1 Khan Academy 2:36 Exponent Properties 2 Khan Academy 5:12 Exponent Properties 3 Khan Academy 2:35 Exponent Properties 4 Khan Academy 3:07

 Strategies and Content Practice Begin(prepare) When we multiply a number by itself, for example, 5 • 5, how can we write this another way? Is there an easier way to write 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2? Engage Exponents are the shorthand way we can show that a number, variable, or algebra expression is multiplied by itself two or more times.For example, in the sample above, 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 shows 2 multiplied by itself 9 times.A shorthand way we can write this is using exponents.                                                  The exponent for of this is:     $\huge \fn_phv {\color{Blue} 2{\color{Red}^{9} }}$The 9 is the exponent.  It is written as a "superscript", that is, it is written to the right and raised up above the number.Numbers, variables, and algebra expressions can all be raised to an exponent.Zero exponents: Any number, variable, or algebra expression raised to the zero exponent is equal to 1.For example, $\huge \fn_phv {\color{Blue} 5{\color{Red}^{0}}= 1}, {\color{Blue} X{\color{Red}^{0}}= 1}, {\color{Blue} (3y){\color{Red}^{0}}= 1}$Negative exponents: Any number, variable, or algebra expression raised to a negative exponent must "jump the bar" (the fraction bar) to turn its negative exponent into a positive exponent.$\huge \fn_phv 7^{-3} ...becomes... \frac{1}{7^{3}}$    $\huge \fn_phv P^{-2} ...becomes... \frac{1}{P^{2}}$   $\huge \fn_phv 4GK^{-5} ...becomes... \frac{4G}{K^{5}}$ Assess(formative) After example problems and videos, try to solve the Practice Worksheets above.  The answers to the practices are on the last page so you can check how well you are doing.Please see me for more help if you are having difficulty with the practices.