Key Equations
Rules of Exponents For nonzero real numbers aa and bb and integers mm and nn |
|
Product rule | am⋅an=am+nam⋅an=am+n |
Quotient rule | aman=am−naman=am−n |
Power rule | (am)n=am⋅n(am)n=am⋅n |
Zero exponent rule | a0=1a0=1 |
Negative rule | a−n=1ana−n=1an |
Power of a product rule | (a⋅b)n=an⋅bn(a⋅b)n=an⋅bn |
Power of a quotient rule | (ab)n=anbn(ab)n=anbn |
Key Concepts
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- 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.
Candela Citations
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