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Exponent Rules
Properties/Solving
Math Bands
100
This is the number of rabbits in 4 years if there are currently 12 and their population doubles every year.
What is 192? 12(2)4=192
100
Evaluate: log525
What is 2?
100
Change 32 = 9 to logarithmic form.
What is log39 = 2?
100
Simplify: x2 * 3x3
What is 3x5?
Multiply the coefficients (no parentheses) and ADD the exponents
100
log(x)-log(y)
What is
log(x/y)?
100
Half a minute to the closest planet.
What is "30 seconds to Mars"?
200
This is the value of your car if it was purchased 5 years ago for $28,000 but depreciates 18% each year.
What is $10,380.72? 28,000(.82)5
200
Evaluate: log5(1/25)
What is -2?
200
Change log464=3 to exponential form.
What is 43=64?
200
Simplify (5x)3
What is 125x3?
200
log(x)+log(y)+log(z)
What is log(xyz)?
200
1/12 of a minute in June or July.
What is "5 seconds of summer".
300
This is the number of years it would take a $2000 investment to triple if the growth rate is 15%.
What is 7.86 years? 2,000(1.15)t=6,000
300
Evaluate: log164
What is 1/2?
300
Change b4=7 to logarithmic form.
What is logb7=4?
300
Simplify: 2(x3)-2
What is
2/x^6?
Power Rule: multiply exponents
Negative Exponent: move to bottom
No parentheses: exponent only applies to the "x"
300
Solve ln(2)+ln(x)-ln(3) = ln 12
What is x = 18?
300
Reddish-Purple Cinco
What is Maroon 5?
400
This is the amount of bacteria remaining after 10 years if the organism had 5000 grams of bacteria originally and the half-life is one year.
What is 4.88 grams? 5,000(1/2)10
400
Evaluate: log1/21/8
What is 3?
400
Change to y=abx form. y=22x-1
What is y=(1/2)4x ?
400
Simplify:
(3w^3)/(6w^5)
What is
1/(2w^2)
?
Quotient Rule: subtract the exponents bottom from top
Negative Exponent Rule: keep on top as negative or move to the bottom as positive
400
Solve log2x + log24 = 3
What is x = 2
400
BlackJack Flyboys
What is 21 pilots?
500
If the half-life of Carbon-14 is 5730 years, this is the amount remaining after 114,600 years if there were originally 2,000 grams.
What is 0.0019 grams ?
2,000(1/2)(114,600/5730)
500
Evaluate: log361/6
What is -1/2?
500
sqrtx=9
Change to y=abx form. y=4(3)3x-2
What is y = (4/9)(27)x ?
500
Simplify
((2^-2x^3y^-4)/(x^0))^2
What is
x^6/(16y^8)?
Power Rule: multiply exponents
Negative exponent: move to bottom
Anything raised to 0 = 1
500
Solve 3x+3 = 45
What is 0.465?
500
Single Commonwealth
What is One Republic?