What is properties of exponents

If a and b are real numbers, and m and n are integers, then. Working with very large or very small numbers can be awkward. Since our number system is base ten we can use powers of ten to rewrite very large or very small numbers to make them easier to work with. Consider the numbers 4, and 0. Using place value, we can rewrite the numbers 4, and 0. If we write the 1, as a power of ten in exponential form, we can rewrite these numbers in this way:.

When a number is written as a product of two numbers, where the first factor is a number greater than or equal to one but less than ten, and the second factor is a power of 10 written in exponential form, it is said to be in scientific notation.

A number is expressed in scientific notation when it is of the form. If we look at what happened to the decimal point, we can see a method to easily convert from decimal notation to scientific notation. In both cases, the decimal was moved 3 places to get the first factor between 1 and How can we convert from scientific notation to decimal form?

If we look at the location of the decimal point, we can see an easy method to convert a number from scientific notation to decimal form. In both cases the decimal point moved 4 places. When the exponent was positive, the decimal moved to the right.

When the exponent was negative, the decimal point moved to the left. When scientists perform calculations with very large or very small numbers, they use scientific notation. Scientific notation provides a way for the calculations to be done without writing a lot of zeros.

We will see how the Properties of Exponents are used to multiply and divide numbers in scientific notation. Multiply or divide as indicated. Access these online resources for additional instruction and practice with using multiplication properties of exponents.

Simplify Expressions Using the Properties for Exponents. In the following exercises, simplify each expression using the properties for exponents. Use the Definition of a Negative Exponent. In the following exercises, simplify each expression using the Product Property. In the following exercises, simplify each expression using the Power Property.

In the following exercises, simplify each expression using the Product to a Power Property. In the following exercises, simplify each expression using the Quotient to a Power Property. In the following exercises, simplify each expression by applying several properties.

Use Scientific Notation. In the following exercises, multiply or divide as indicated. Write your answer in decimal form. What is wrong with her reasoning? When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative? Summary By the end of this section, you will be able to: Simplify expressions using the properties for exponents Use the definition of a negative exponent Use scientific notation.

Note Before you get started, take this readiness quiz. If you missed this problem, review [link]. Simplify Expressions Using the Properties for Exponents Remember that an exponent indicates repeated multiplication of the same quantity. Answer To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator. For example, 4 1.

Scientific notation is the standard form of writing very large numbers or very small numbers. In this, numbers are written with the help of decimal and powers of A number is said to be written in scientific notation when a number from 0 to 9 is multiplied by a power of In the case of a number greater than 1 , the power of 10 will be a positive exponent, while in the case of numbers less than 1 , the power of 10 will be negative.

Let's understand the steps for writing numbers in scientific notation:. To learn more about the use of exponents in writing scientific notation of numbers, visit the following articles:. Example 1: The dimensions of a wardrobe are given in terms of exponents such as x 5 units, y 3 units, and x 8 units.

Find its volume. The given dimensions of the wardrobe are in form of exponents, i. Therefore, the volume of the wardrobe is x 13 y 3 cubic units. Example 2: In a forest, each tree has about 5 7 leaves and there are about 5 3 trees in the forest. Find the total number of leaves in terms of exponents. Therefore, the total number of leaves is 5 An exponent is a number that is placed as a superscript over a number.

In other words, it indicates that the base is raised to a certain power. The exponent is also called by other names like index and power. If m is a positive number and n is its exponent, then m n means m is multiplied by itself for n times. Laws of exponents are some rules that we use to do calculations involving exponents. These rules help us to calculate quickly.

Laws of exponents or few important properties of exponents are listed below:. In real life, we use the concept of exponents to write numbers in a simplified manner and in a short way. Repeated multiplication can be easily written with the help of exponents. Also, we use exponents to write larger numbers, for example, the distance of the moon from earth, the number of bacteria present on a surface, etc. Exponents cannot be added. We can only add like terms terms having the same exponent and same variable.

But, in the case of the multiplication of terms with the same variables, we add the exponents of the variable to multiply. In earlier chapters we introduced powers. More classes on this subject Algebra 1 Exponents and exponential functions: Exponential growth functions.

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