Exponents and Scientific Notation

Scientific Notation

A number is written in scientific notation when it is represented as the product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10 .

Dividing Powers with the SAME Base

Always subtract the exponent of the divisor (denominator) from the exponent of the dividend (numerator)

Adding and Subtracting Numbers in Scientific Notation

Find the sum or difference. Write your answer in scientific notation

Multiplying Powers with the SAME Base

Keep the base and add the exponents then simplify

Writing Numbers in Scientific Notation

Step 1: Move the decimal point so it is located to the right of the leading nonzero digit. Step 2: Count the number of places you moved the decimal point. This indicates the exponent of the power of 10, as shown below.

Writing Numbers in Standard Form

The absolute value of the exponent indicates how many places to move the decimal point.

Exponent

The exponent of a power indicates the number of times the base is used as a factor

Quotient of Powers Property

To divide powers with the same base, subtract their exponents

Power of a Power Property

To find a power of a power, multiply the exponents

Power of a Product Property

To fond a power of a product, find the power of each factor and multiply

Product of Powers Property

To multiply powers with the same base, add their exponents

Power

is a product of repeated factors

Base

the base of a power is the common factor