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Law of Exponents
Exponential Equation 1
Exponential Equation 2
Transformation
Other
100
1
(3x^4y^3)^0
100
What is: 4^2x+3 = 4^-9
x=-6
100
What is: 3^7x-3 = 9^2x
x=1
100
f(x)=3*(1/2)^(x-2)-1
Stretch Decay Right 2 Down 1
100
5^-3r = 5^-2r-3
r=3
200
What is Common base, keep the base and add the exponents
Product Rule
200
What is: 11^4x-9 = 11^-2x+4
_ x=2.16
200
8^-3x+5 = 32^-5x-7
x=-3.125
200
f(x)=4*2^(x+2)+2
Stretch Growth Left 2 Up 2
200
(4xy)^-2
1/16x^2y^2
300
Common base, subtract exponents. *Put the answer in the numerator or denominator depending on where the higher power is located.
Quotient Rule
300
What is: 2^6x-5 = 2^3
_ x=1.3
300
3^x+7 = 1
x=-7
300
f(x)=-4*2^(x-2)-1
Reflection Stretch Growth Right 2 Up 2
300
Bases are different- use exponents and change to have common bases.
Scenario #2
400
(2x^4y^2)^3
8x^12y^6
400
What is: 3^-2x+3 = 3^5
x=-1
400
16^x = 64^x+1
x=-3
400
f(x)=-2*(1/2)^(x-2)+2
Reflection Stretch Decay Right 2 Up 2
400
Common bases- set exponents equal to each other & solve for the variable
Scenario #1
500
2x^3/6x^2 *Remember Reduce.
1x/3
500
What is: 7^x-8 = 7^x-9
No Solution
500
7^2x+3 = 49^x-1
No Solution
500
f(x)=2*(1/3)^(x+1)-2
Stretch Decay left 1 Down 2
500
8m^-4
8/m^4