## Rewrite each number in exponential notation using 2 as the base

By Yang Kuang, Elleyne Kase. Fractional exponents are roots and nothing else. In this example, you find the root shown in the denominator the cube root and then take it to the power in the numerator the first power. You can choose either method:. Either way, the equation simplifies to 4.

Depending on the original expression, though, you may find the problem easier if you take the root first and then take the power, or you may want to take the power first.

Because the solution is written in exponential form and not in radical form, as the original expression was, rewrite it to match the original expression. Typically, your final answer should be in the same format as the original problem; if the original problem is in radical form, your answer should be in radical form.

And if the original problem is in exponential form with rational exponents, your solution should be as well. Mary Jane Sterling aught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois for more than 30 years.

### Expanded Form and Word Form Calculator

How to Rewrite Radicals as Exponents. About the Book Author Mary Jane Sterling aught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois for more than 30 years.Expanded form calculator shows expanded forms of a number including expanded notation form, expanded factor form, expanded exponential form and word form. Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits.

When numbers are separated into individual place values and decimal places they can also form a mathematical expression. Standard Form : 5, Word Form: five thousand, three hundred twenty-five. Note that in England and Great Britain the phrase "standard form" refers to the scientific number notation that the US calls "scientific notation. See our Numbers to Words Converter to get word form names of numbers. This calculator is particularly helpful for finding the word form of very small decimals.

Basic Calculator. Expanded Form and Word Form Calculator. Expanded Form Calculator. Find the expanded forms of:. Answer: Standard Form: 23, Expanded forms can be written like a sentence or stacked for readability as they are here.

Practice: Rewrite exponential expressions. Equivalent forms of exponential expressions. Practice: Equivalent forms of exponential expressions. Next lesson. Current timeTotal duration Math: HSN. Google Classroom Facebook Twitter. Video transcript - [Voiceover] What I hope to do in this video is get some practice simplifying some fairly hairy exponential expressions.

So let's get started. Let's say that I have the expression 10 times nine to the t over two plus two power, times five to the three t.

And what I wanna do is simplify this as much as possible, and preferably get it in the form of A times B to the t. And like always, I encourage you to pause this video and see if you can do this on your own using exponent properties, your knowledge, your deep knowledge of exponent properties. All right, so let's work through this together, and it's really just about breaking the pieces up. So 10, I'll just leave that as 10 for now, there doesn't seem to be much to do there.

But there's all sorts of interesting things going on here. So nine to the t over two, plus two, so this right over here, I could break this up, using the fact that, and I'll just write the properties over here. If I have nine to the a plus b power, this is the same thing as nine to the a, times nine to the b power. And over here I have nine to the t over two, plus two, so I could rewrite this as nine to the t over two power, times nine squared. All right, now let's move over to five to the three t.

Well, if I have a to the bc, so you could view this as five to the three times t, this is the same thing as a to the b, and then that to the c power. So I could write this as, this is going to be the same thing as five to the third, and then that to the t power. And the whole reason I did that is well this is just going to be a number, then I'm going to have some number to the t power.

I want to get as many things just raised to the t power as possible, just to see if I can simplify this thing. So this character right over here is going to be Nine squared is Five to the third power, 25 times five, that's So we're making good progress and so the only thing we really have to simplify at this point is nine to the t over two. And actually let me do that over here. Nine to the t over two. Well that's the same thing as nine to the one half times t.

And by this property right over here, that's the same thing as nine to the one, nine to the one half And then that to the t power.

## How to Rewrite Radicals as Exponents

So what's nine to the one half? Well that's three, so this is going to be equal to three to the t power.The product of factors is also displayed in this table. How long do you think that would take? Writing 2 as a factor one million times would be a very time-consuming and tedious task. Exponential notation is an easier way to write a number as a product of many factors.

For example, to write 2 as a factor one million times, the base is 2, and the exponent is 1, We write this number in exponential form as follows:. So far we have only examined numbers with a base of 2.

Let's look at some examples of writing exponents where the base is a number other than 2. Exponential notation makes it easier to write a number as a factor repeatedly. A number written in exponential form is a base raised to an exponent. The exponent tells us how many times the base is used as a factor. Directions: Read each question below. Do not use commas in your answers, just digits. By signing up, you agree to receive useful information and to our privacy policy.

Shop Math Games. Skip to main content. Search form Search. Exercises Directions: Read each question below. What israised to the zero power? What is raised to the first power? The number 81 is 3 raised to which power?

Elementary Math Lessons.Enter expression, e. Enter a set of expressions, e. Enter equation to solve, e. Enter equation to graph, e. Number of equations to solve: 2 3 4 5 6 7 8 9 Sample Problem Equ. Enter inequality to solve, e. Enter inequality to graph, e. Number of inequalities to solve: 2 3 4 5 6 7 8 9 Sample Problem Ineq. Please use this form if you would like to have this math solver on your website, free of charge. The system is not has functional as I wanted or expected, and there are several problems it will not solve, or certain problems will freeze up the system. The program is OK but there are too many limitations and several technical issues. It took three e-mail from their tech support just to activate the program.

Theresa Saunders, OR. I was down to a C and worried when I found your software. I credit your program for most of what I learned. Thanks for the quick reply. Joe Johnson, OH.

### Rewriting exponential expressions as A⋅Bᵗ

The newest release of your software is tremendous. Besides the GUI I particularly liked the "wizards" that make entry of geometry type problems so much easier. I haven't yet used the more advanced features function operations etcbut this will become handy once I get into College Algebra. Monica, TX. Expression Equation Inequality Contact us. Solve Graph System. Math solver on your site. Theresa Saunders, OR Wonderful tool for a new algebra student. Joe Johnson, OH The newest release of your software is tremendous.

Sample Problem. Find GCF. Find LCM. Depdendent Variable. Number of equations to solve:. Solve for:. Auto Fill. Dependent Variable.Learning Objective s. A common language is needed in order to communicate mathematical ideas clearly and efficiently. Exponential notation is one example. It was developed to write repeated multiplication more efficiently.

For example, growth occurs in living organisms by the division of cells.

One type of cell divides 2 times in an hour. This can be written more efficiently as 2 Exponential Vocabulary. The 10 in 10 3 is called the base. The 3 in 10 3 is called the exponent. The expression 10 3 is called the exponential expression. Its value will depend on the value of b. The exponent applies only to the number that it is next to.

So in the expression xy 4only the y is affected by the 4. You can see that there is quite a difference, so you have to be very careful!

Evaluating Expressions Containing Exponents. Evaluating expressions containing exponents is the same as evaluating any expression. You substitute the value of the variable into the expression and simplify. First, evaluate anything in P arentheses or grouping symbols. Next, look for E xponents, followed by M ultiplication and D ivision reading from left to rightand lastly, A ddition and S ubtraction again, reading from left to right.

Then evaluate, using order of operations. Substitute 4 for the variable x. Evaluate 4 3. Notice the difference between the example above and the one below. The addition of parentheses made quite a difference!

A 1, Do not apply the negative sign until after you have evaluated the expression 6 4. Then apply the negative sign.We use exponential notation to write repeated multiplication. Knowing the names for the parts of an exponential expression or term will help you learn how to perform mathematical operations on them. Its value will depend on the value of b. The exponent applies only to the number that it is next to.

The x in this term is a coefficient of y. You can see that there is quite a difference, so you have to be very careful!

The following examples show how to identify the base and the exponent, as well as how to identify the expanded and exponential format of writing repeated multiplication. The exponent in this term is 2 and the base is 7. The exponent on this term is 3, and the base is x, the 2 is not getting the exponent because there are no parentheses that tell us it is.

This term is in its most simplified form. In the following video you are provided more examples of applying exponents to various bases. Evaluating expressions containing exponents is the same as evaluating the linear expressions from earlier in the course. You substitute the value of the variable into the expression and simplify. First, evaluate anything in Parentheses or grouping symbols.

Next, look for Exponents, followed by Multiplication and Division reading from left to rightand lastly, Addition and Subtraction again, reading from left to right.

Then evaluate, using order of operations. In the example below, notice the how adding parentheses can change the outcome when you are simplifying terms with exponents. The addition of parentheses made quite a difference! Parentheses allow you to apply an exponent to variables or numbers that are multiplied, divided, added, or subtracted to each other.

Whether to include a negative sign as part of a base or not often leads to confusion. To evaluate 1you would apply the exponent to the three first, then apply the negative sign last, like this:. To evaluate 2you would apply the exponent to the 3 and the negative sign:. The key to remembering this is to follow the order of operations.

The first expression does not include parentheses so you would apply the exponent to the integer 3 first, then apply the negative sign. The second expression includes parentheses, so hopefully you will remember that the negative sign also gets squared. In the next sections, you will learn how to simplify expressions that contain exponents. Come back to this page if you forget how to apply the order of operations to a term with exponents, or forget which is the base and which is the exponent!

In the following video you are provided with examples of evaluating exponential expressions for a given number. Exponential notation was developed to write repeated multiplication more efficiently. There are times when it is easier or faster to leave the expressions in exponential notation when multiplying or dividing. What happens if you multiply two numbers in exponential form with the same base? Notice that 7 is the sum of the original two exponents, 3 and 4.

And, once again, 8 is the sum of the original two exponents.