# Rewrite a rational exponent

### Radical expressions and rational exponents worksheet

OR Create the numerator first and then the denominator. Squaring and square rooting are inverse operations. The Definition of : , this says that if the exponent is a fraction, then the problem can be rewritten using radicals. Is this going to be equivalent? Five over six. Look for and express regularity in repeated reasoning. Sometimes partners within the class help each other. Let's see two examples: 1. If x is a real number and m and n are positive integers: The denominator of the fractional exponent becomes the index root of the radical. Why TWO possible results? Notice that the denominator of the fraction becomes the index of the radical. Notice that the denominator of the fraction becomes the index of the radical and the numerator becomes the power inside the radical. And I forgot to tell you in the last one, but pause this video as well and see if you can work it out on This gives you 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 so, that is going to be equal to x to the d.

Five over six. And I forgot to tell you in the last one, but pause this video as well and see if you can work it out on Take a look at some steps that illustrate this process.

That's what we have right over here, so that one is definitely equivalent. If we apply the rules of exponents, we can see how there are two possible ways to convert an expression with a fractional exponent into an expression in radical form.

Well, here, let's just start rewriting the root as an exponent. Let's do one more of these. The purpose of this Warm up is to introduce students to rational exponents.

The following equation is true for g greater than or equal to zero, and d is a constant.

## Exponents and radicals

When you multiply monomials with the same base, you add the exponents. That's what we have right over here, so that one is definitely equivalent. So, the key here is when you're taking the reciprocal of something, that's the same thing as raising it to the negative of that exponent. And then, if you multiply these exponents, you get what we have right over there. Notice that the denominator of the fraction becomes the index of the radical and the numerator becomes the power inside the radical. Alright, this is interesting. The purpose of this Warm up is to introduce students to rational exponents. Five over six. Create the denominator first and then the numerator. The Definition of : , this says that if the exponent is a fraction, then the problem can be rewritten using radicals. Let's do a few more of these, or similar types of problems dealing with roots and fractional exponents.

Properties of exponents rational exponents Video transcript - [Voiceover] We're asked to determine whether each expression is equivalent to the seventh root of v to the third power. Convert from Exponential to Radical Form: Remember the denominator of the fractional exponent will become the root of the radical, and the numerator will become the power.

## How to rewrite expressions using rational exponents

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. Well, a good way to figure out if things are equivalent is to just try to get them all in the same form. Is this going to be equivalent? The purpose of this Warm up is to introduce students to rational exponents. Students should be familiar with the Laws of Exponents to apply to these problems. Only move the negative exponents. This is similar to reducing fractions; when you subtract the powers put the answer in the numerator or denominator depending on where the higher power was located. Why TWO possible results? The Power Property - multiply exponents times exponents of powers to other powers. So, this is not going to be equivalent for all v's, all v's for which this expression is defined. Convert from Exponential to Radical Form: Remember the denominator of the fractional exponent will become the root of the radical, and the numerator will become the power. In the last section I present to students how to write as a single rational exponent by finding a common denominator for the exponents and then simplifying.

So, the key here is when you're taking the reciprocal of something, that's the same thing as raising it to the negative of that exponent. Negative Exponent Rule:this says that negative exponents in the numerator get moved to the denominator and become positive exponents. I raise something to an exponent and then raise that whole thing to another exponent, I can just multiply the exponents.

Sometimes partners within the class help each other.

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