Properties of
Exponents
Exponents
Any number or expression raised to the power of zero is always equal to _______.
1
What does a represent in an exponential growth or an exponential decay function?
The initial (starting) amount
How do you solve an exponential equation when both sides have the same base?
Set the exponents equal to each other
Geometric sequences have a common _______ between consecutive terms.
Ratio
Name the song:
"Cause the players gonna play, play, play, play, play..."
Shake It Off
Simplify the expression. Write your answer using only positive exponents.
2^4*2^3
128
Does the following function represent exponential growth or exponential decay? Explain.
y=0.25(1.56)^t
Exponential Growth – the number is parentheses is larger than 1
Solve the exponential equation.
4^(5x+9)=4^(x+1)
x = –2
Identify the common ratio of the following geometric sequence.
3, 18, 108, 648, . . .
r = 6
What is Taylor's second album??
Fearless
Simplify the expression. Write your answer using only positive exponents.
(x^5)^-3
1/x^15
Does the following function represent exponential growth or exponential decay? Explain.
y=–6(3/4)^t
Exponential Decay – the number in parentheses is between 0 and 1.
How do you solve an exponential equation when both sides have a different base?
Rewrite one (or both) sides using the same base
Identify the common ratio of the following geometric sequence.
144, –72, 36, –18, . . .
r = –½
What is the name of Taylor's new album?
Double points if you know when it will be released!
The Tortured Poets Department
April 19th
Simplify the expression. Write your answer using only positive exponents.
4x^0y^-3
4/y^3
Identify the percent rate of change of the following exponential function.
y=0.25(1.56)^t
r = 56%
Solve the exponential equation.
25^(x)=5^(x-3)
x = –3
Write an equation for the nth term of the geometric sequence.
2, 8, 32, 128, . . .
a_n=2(4)^(n-1)
What are the names of Taylor Swift's cats?
Benjamin, Meredith, Olivia
Simplify the expression. Write your answer using only positive exponents.
((2x^4y^2)/(5xy^6))^2
(4x^6)/(25y^8)
Identify the percent rate of change of the following exponential function.
y=-6(3/4)^t
r = 25%
Solve the exponential equation.
(1/4)^(x)=256
x = –4
Find the 6th term of the following geometric sequence.
0.6, –3, 15, –75, . . .
a_6=-1,875
How long was Taylor Swift shown on TV at the Super Bowl?
ONLY 54 seconds