## 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 $\frac{{a}^{m}}{{a}^{n}}={a}^{m-n}$ Power rule ${\left({a}^{m}\right)}^{n}={a}^{m\cdot n}$ Zero exponent rule ${a}^{0}=1$ Negative rule ${a}^{-n}=\frac{1}{{a}^{n}}$ Power of a product rule ${\left(a\cdot b\right)}^{n}={a}^{n}\cdot {b}^{n}$ Power of a quotient rule ${\left(\frac{a}{b}\right)}^{n}=\frac{{a}^{n}}{{b}^{n}}$

## 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.
• Scientific notation uses powers of 10 to simplify very large or very small numbers.
• Scientific notation may be used to simplify calculations with very large or very small numbers.

## Glossary

scientific notation a shorthand notation for writing very large or very small numbers in the form $a\times {10}^{n}$ where $1\le |a|<10$ and $n$ is an integer