Exponential notation is a way of representing a number as a product of a base and an exponent. The exponent tells us how many times the base is multiplied by itself. For example, in the expression 5^3, 5 is the base and 3 is the exponent. This means 5 is multiplied by itself 3 times: 5 * 5 * 5 = 125.

- When multiplying two numbers with the same base, add the exponents: a^m * a^n = a^(m + n)
- When dividing two numbers with the same base, subtract the exponents: a^m / a^n = a^(m - n)
- When raising a power to another power, multiply the exponents: (a^m)^n = a^(m * n)

Scientific notation is a way of expressing very large or very small numbers in a more compact form. It is written in the form a x 10^n, where 1 ≤ a < 10 and n is an integer. For example, the speed of light is approximately 299,792,458 meters per second. In scientific notation, this is written as 2.99792458 x 10^8.

To convert a number to scientific notation, follow these steps:

- Move the decimal point to the right or left to create a number between 1 and 10
- Count the number of places the decimal point was moved. This number becomes the exponent of 10

To convert a number from scientific notation to standard form, simply multiply the coefficient by 10 raised to the power of the exponent.

Here are some practice problems to help you master exponential and scientific notation:

- Calculate the following using exponential notation: 2^4, 3^2, 5^3
- Simplify the following using exponential notation: 2^3 * 2^5, 4^7 / 4^4, (3^2)^4
- Express the following numbers in scientific notation: 480,000,000, 0.0000075, 9,600,000,000,000
- Convert the following numbers from scientific notation to standard form: 6.4 x 10^3, 9.75 x 10^-5, 2.1 x 10^6

Practice these problems to improve your understanding of exponential and scientific notation.

Study GuideExponential & Scientific Notation Worksheet/Answer key

Exponential & Scientific Notation Worksheet/Answer key

Exponential & Scientific Notation Worksheet/Answer key

Exponential & Scientific Notation Worksheet/Answer key

Exponential & Scientific Notation Worksheet/Answer key

Exponential & Scientific Notation Worksheet/Answer key

Exponential & Scientific Notation Vocabulary/Answer key

Exponential & Scientific Notation

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.