Summary: Review | College Algebra Corequisite

Module 5: Exponential and Logarithmic Functions

Summary: Review

Key Equations

Rules of Exponents For nonzero real numbers $a$ and $b$ and integers $m$ and $n$
Product rule	${a}^{m}\cdot {a}^{n}={a}^{m+n}$
Quotient rule	$\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n}$
Power rule	${\left({a}^{m}\right)}^{n}={a}^{m\cdot n}$
Zero exponent rule	${a}^{0}=1$
Negative rule	${a}^{-n}=\dfrac{1}{{a}^{n}}$
Power of a product rule	${\left(a\cdot b\right)}^{n}={a}^{n}\cdot {b}^{n}$
Power of a quotient rule	${\left(\dfrac{a}{b}\right)}^{n}=\dfrac{{a}^{n}}{{b}^{n}}$

Key Concepts

- Products of exponential expressions with the same base can be simplified by adding exponents.
- Quotients of exponential expressions with the same base can be simplified by subtracting exponents.
- Powers of exponential expressions with the same base can be simplified by multiplying exponents.
- An expression with exponent zero is defined as 1.
- An expression with a negative exponent is defined as a reciprocal.
- The power of a product of factors is the same as the product of the powers of the same factors.
- The power of a quotient of factors is the same as the quotient of the powers of the same factors.
- The rules for exponential expressions can be combined to simplify more complicated expressions.
- Corresponding input and output pairs of a function each represent a point on the graph of the function.
- Each point contained on the graph of a function satisfies the equation of a function.