Exponents Flashcards
What is an Exponential Relationship?
A relationship where a variable grows or decreases at a constant rate, typically expressed in the form y = a * b^x
Here, ‘a’ is a constant, ‘b’ is the base, and ‘x’ is the exponent.
Define Linear Relationship.
A relationship where the change in one variable is proportional to the change in another, represented by a straight line on a graph.
What is the equation for an exponential relationship?
y = 2^x
This represents a basic exponential function.
What is the expanded form of 5^2?
5 x 5 = 25
Fill in the blank: 5^2 = ______.
25
What happens when the base is negative and the exponent is even?
The result is positive.
What happens when the base is negative and the exponent is odd?
The result is negative.
What is the result of (-x)^n when n is even?
Positive.
What is the result of -x^n when n is odd?
Negative.
What is the base in an exponential form?
The number that is raised to a power.
What is the Product of a Power Law?
When multiplying powers together with the same base, you can add the exponents
Example: a^m × a^n = a^(m+n)
What is the Quotient of a Power Law?
When dividing powers of the same base, you can subtract the exponents
Example: a^m ÷ a^n = a^(m-n)
What does the zero rule state?
When the exponent of a power is zero, the value will automatically equal 1
Example: a^0 = 1
What is the Power of a Power Law?
When a power is raised to an exponent, it can be simplified by multiplying the exponents
Example: (a^m)^n = a^(m*n)
Fill in the blank: When multiplying powers together with the same base, you can ______ the exponents.
add
Fill in the blank: When dividing powers of the same base, you can ______ the exponents.
subtract
True or False: a^0 = 0.
False
True or False: (a^m)^n = a^(m+n).
False
What is the Power of a Product Law?
When you have an existing multiplication statement attached to an exponent, you can rewrite each factor as a power
The law is expressed as (a * b)^m = a^m * b^m
What does the Power of a Quotient Law state?
When a quotient is raised to a power, you can rewrite each number as a power
The law is expressed as (a/b)^n = a^n / b^n
