Exponential Functions and Laws of Exponents

These flashcards cover key concepts and laws related to exponential functions as outlined in the lecture notes.

What is the result of multiplying two numbers with the same base, a^m * a^n?

a^(m+n)

What is the result of dividing two numbers with the same base, a^m / a^n?

a^(m-n)

What is the result when raising a power to another power, (a^m)^n?

a^(m*n)

What is the power of a product, (ab)^n?

a^n * b^n

What is the power of a quotient, (a/b)^n?

a^n / b^n

What is the value of n if 8^3 = 2^n?

n = 9

How do you express x^0?

x^0 = 1, for x ≠ 0

What is the expression for (xy)^3?

x^3 * y^3

What is the expression for 3x^4y^5 / (xy^3)?

3x^3y^2

What is the simplified form of (4x)^3?

64x^3