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# Rules of Exponents

break down all the rules of working with exponents so students can see WHY the rules work

by

Tweet## Katherine McDonald

on 9 July 2010#### Transcript of Rules of Exponents

rule 1: x^a * x^b = x^(a+b) example: 2^2 * 2^3 = (2*2)*(2*2*2) = 2^5 = 2^(2+3)

rule 2: x^a / x^b = x^(a-b) example: 5^4 / 5^2 = (5*5*5*5)/(5*5) = 5^2 = 5^(4-2) rule 3: (x^a)^b = x^(a*b) EXPONENTS rules of example: (3^2)^3 = {3^2)*{3^2)*(3^2) =

(3*3)*(3*3)*(3*3) = 3^6 = 3^(2*3) rule 4: (xy)^a = x^a * y^a example: {5x)^4 = {5x)*{5x}*(5x)*(5x) = 5*5*5*5*x*x*x*x = 5^4 * x^4 rule 5: (x/y)^a = (x^a)/(y^a) example: (2/7)^3 = (2/7)*{2/7)*(2/7)=

2*2*2*(1/7)*(1/7)*(1/7) = (2^3)*(1/7)^3 = (2^3)/(7^3) rule 6: x^-a = 1/(x^a) example: 2^-2 = 1/(2^2) = 1/(2*2) = 1/4 note: negative exponents mean to take the inverse (reciprocal) of the base...

not to produce a negative answer rule 7: x^0 = 1 example: 1,000,000^0 = 1 how?

5^4 / 5^4 = 5^(4-4) = 5^0 =1

5^4 / 5^4 = (5*5*5*5) / (5*5*5*5) =1 try: 4^2 * 4^10 = 4^(2+10)= 4^12 try: 3^6 / 3^3 = 3^(6-3) = 3^3 try: (2x)^4 = 2^4 * x^4 try: (x/6)^2 = (x^2) / (6^2) try: 4^-6 = 1/ (4^6) try: 6^0 =1 try: (3^4)^2 = 3^(4*2) = 3^8 = a power of

to the X degree E base exponent

Full transcriptrule 2: x^a / x^b = x^(a-b) example: 5^4 / 5^2 = (5*5*5*5)/(5*5) = 5^2 = 5^(4-2) rule 3: (x^a)^b = x^(a*b) EXPONENTS rules of example: (3^2)^3 = {3^2)*{3^2)*(3^2) =

(3*3)*(3*3)*(3*3) = 3^6 = 3^(2*3) rule 4: (xy)^a = x^a * y^a example: {5x)^4 = {5x)*{5x}*(5x)*(5x) = 5*5*5*5*x*x*x*x = 5^4 * x^4 rule 5: (x/y)^a = (x^a)/(y^a) example: (2/7)^3 = (2/7)*{2/7)*(2/7)=

2*2*2*(1/7)*(1/7)*(1/7) = (2^3)*(1/7)^3 = (2^3)/(7^3) rule 6: x^-a = 1/(x^a) example: 2^-2 = 1/(2^2) = 1/(2*2) = 1/4 note: negative exponents mean to take the inverse (reciprocal) of the base...

not to produce a negative answer rule 7: x^0 = 1 example: 1,000,000^0 = 1 how?

5^4 / 5^4 = 5^(4-4) = 5^0 =1

5^4 / 5^4 = (5*5*5*5) / (5*5*5*5) =1 try: 4^2 * 4^10 = 4^(2+10)= 4^12 try: 3^6 / 3^3 = 3^(6-3) = 3^3 try: (2x)^4 = 2^4 * x^4 try: (x/6)^2 = (x^2) / (6^2) try: 4^-6 = 1/ (4^6) try: 6^0 =1 try: (3^4)^2 = 3^(4*2) = 3^8 = a power of

to the X degree E base exponent