Key Concepts & Glossary

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	${\left(\frac{a}{b}\right)}^{n}=\frac{{a}^{n}}{{b}^{n}}$

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.

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