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In this tutorial we are going to combine two ideas that have been discussed in earlier tutorials: exponents and radicals. We will look at how to rewrite, simplify and evaluate these expressions that contain rational exponents. What it boils down to is if you have a denominator in your exponent, it is your index or root number. So, if you need to, review radicals covered in Tutorial 37: Radicals. Also, since we are working with fractional exponents and they follow the exact same rules as integer exponents, you will need to be familiar with adding, subtracting, and multiplying them. If fractions get you down you may want to go to Beginning Algebra Tutorial 3: Fractions. To review exponents, you can go to Tutorial 23: Exponents and Scientific Notation Part I andTutorial 24: Exponents and Scientific Notation Part II. Let's move onto rational exponents and roots.
After completing this tutorial, you should be able to:
- Rewrite a rational exponent in radical notation.
- Simplify an expression that contains a rational exponent.
- Use rational exponents to simplify a radical expression.
These are practice problems to help bring you to the next level. It will allow you to check and see if you have an understanding of these types of problems. Math works just like anything else, if you want to get good at it, then you need to practice it. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. In fact there is no such thing as too much practice.
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
What else can I help you with?
Rewrite the following expressions using the Commutative Property?
a+b=
How do you rewrite five to the negative 4Th power so that the exponent is positive?
5-4 = 1/54 = (1/5)4 or 0.24
What set of numbers does a mixed fraction belong to?
A mixed fraction is a rational number because you can rewrite it as one integer over another.
how do you rewrite 8x8x8x8x8 as a exponent?
8^5
How do you express x to the power of negative 2 as a fraction?
To express x to the power of negative 2 as a fraction, you can rewrite it as 1 over x squared. This is because any number raised to a negative exponent is equivalent to its reciprocal raised to the positive exponent. Therefore, x to the power of negative 2 is the same as 1 over x squared.
How do you rewrite or convert a rational exponent to a radical form?
pa/b = (pa)1/b = bth root of (pa)
Rewrite the following expressions using the Commutative Property?
a+b=
How do you rewrite these expressions using numbers and mathematical symbol?
16-2
How do you rewrite rational numbers as decimals?
Perform long division of the ratio.
Rewrite 8x8 using an exponent?
8 to the power of 2, like 8^2
When replacing variable with constant?
Rewrite the expressions, equations or inequalities where the constant takes the place of each occurrence of the variable.
How do you rewrite five to the negative 4Th power so that the exponent is positive?
5-4 = 1/54 = (1/5)4 or 0.24
How turn a negative exponent into a decimal?
To convert a negative exponent into a decimal, first rewrite the expression by taking the reciprocal of the base raised to the positive exponent. For example, ( a^{-n} ) can be rewritten as ( \frac{1}{a^n} ). Then, calculate the value of ( a^n ) and take its reciprocal to find the decimal representation. This process effectively transforms the negative exponent into a positive one in the denominator.
How do you write an expression using a single exponet?
To write an expression using a single exponent, you can apply the properties of exponents to combine terms. For instance, if you have (a^m \times a^n), you can rewrite it as (a^{m+n}). Similarly, if you have a fraction like (\frac{a^m}{a^n}), it can be expressed as (a^{m-n}). By using these properties, you can simplify expressions to a single exponential form.
What set of numbers does a mixed fraction belong to?
A mixed fraction is a rational number because you can rewrite it as one integer over another.
how do you rewrite 8x8x8x8x8 as a exponent?
8^5
How do you find equivalent expressions that have a lcd?
To find equivalent expressions with a least common denominator (LCD), first identify the denominators of the given expressions. Factor each denominator to find the least common multiple, which will serve as the LCD. Next, rewrite each expression so that its denominator matches the LCD by multiplying the numerator and denominator by the necessary factors. Finally, simplify the resulting expressions if needed, ensuring they remain equivalent to the original expressions.
