Exponents

Exponents are algebraic operations that allow us to express extremely large and small numbers. The exponent refers to how many times a number is multiplied by itself.

Exponent Rules

_________ of Exponents	Definition
Product Rule	$a^m \times a^n = a^{m + n}$
Quotient Rule	$\frac{a^m}{a^n} = a^{m - n}$
Power Rule	$(a^m)^n = a^{m \times n}$
Zero Exponent Rule	$a^0 = 1$
Negative Rule	$a^{-n} = \frac{1}{a^n}$
Power of Product Rule	$(ab)^n = a^nb^n$
Power of Quotient Rule	$(\frac{a}{b})^n = \frac{a^n}{b^n}$

Scientific Notation

We can use scientific notation as shorthand method of writing very small and very large numbers. A number written using this method is in the form $a \times 10^n$, where $1 \leq |a| < 10$ and $n$ is an integer.

The method is to move the decimal point left or right of a given number till only 1 digit is before the decimal point. Count the number of places moved and thats the value of $n$ in $10^n$. If you moved the decimal to the right, add a negative sign to $n$.

To go from scientific to standard, move the decimal $n$ places to the right if $n$ is positive or $n$ places to the left if $n$ is negative and add zeros as needed.