Exponents and Exponential Functions

What is the Product of Powers property?

When multiplying numbers with the same base, ADD the exponents: a^m * a^n = a^(m+n)

What is the Quotient of Powers property?

When dividing numbers with the same base, SUBTRACT the exponents: a^m / a^n = a^(m-n)

What is the Power of a Power property?

If raising a power to a power, MULTIPLY the exponents: (a^m)^n = a^(m*n)

What is the Zero Exponent property?

Any non-zero number raised to the zero power is equal to 1: a^0 = 1

How do you rewrite a Negative Exponent?

Place the power in the denominator to rewrite it as a positive exponent: a^-n = 1 / a^n

What is a rational exponent?

An exponent written as a fraction.

How do you convert from radical form to a rational exponent?

The nth root of x^m equals x^(m/n).

What is the first step in solving equations with rational exponents?

Isolate the term(s) raised to a power.

How do you eliminate a rational exponent when solving an equation?

Raise both sides of the equation to the RECIPROCAL power.

What are the two main properties of Radicals?

1. Product Prop: nth root of (a*b) = (nth root of a) * (nth root of b) | 2. Quotient Prop: nth root of (a/b) = (nth root of a) / (nth root of b)

How do Linear and Exponential functions differ in growth rate?

Linear functions increase/decrease at a constant rate; Exponential functions increase/decrease faster over time.

What is the connection between Linear Functions and sequences?

They connect to Arithmetic Sequences where the common difference 'd' is the slope.

What is the connection between Exponential Functions and sequences?

They connect to Geometric Sequences where the common ratio 'r' is the base 'b'.