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## How To Simplify Rational Exponents

This lesson covers how to simplify rational exponents in exponent form using the properties of exponents and is the second part to my blog post on Radical Form and Rational Exponents. Working with rational is an algebra 2, but the properties of exponents learned in algebra 1 with integer exponents apply. Here is a list of the properties of exponents for review:

• Product of Powers  $a^{m} \cdot a^{n} = a^{m+n}$
• Power of Powers   $(a^{m})^{n} = a^{mn}$
• Power of a Monomial $(ab)^{m} = a^{m}b^{m}$
• Negative Exponent $a^{-n} = \frac{1}{a^{n}}$
• Quotient of Powers $\frac{a^{m}}{a^{n}} = a^{m-n}$
• Power of a Quotient  $(\frac{a}{b})^m = \frac{a^{m}}{b^{m}}$

The first section of the video reviews the above list of properties.

The second part of the video (example 4T part a) simplifying the expression $(-32)^{\frac{3}{5}}$. There are two methods to simplify this expression. The first method that is modeled is using the properties of exponents and the second method modeled is converting the rational exponent into a radical and a power. Either method that is used requires the problem solver to figure out “what number can be raised to the n power to get the original number?”

Example 4T part b is similar to part a, but the exponent is expressed as a mixed decimal number. To evaluate this expression, the mixed decimal number needs to be converted to an improper fraction. Then either method modeled in part a can be applied.

Finally, example 5T involve a more complicated expression to simplify and it involves negative exponents. The key concept to know is that all negative exponents need to be expressed as positive exponents.

Enjoy the video and feel free to post any questions in the comment section.

Regards,

Mr. Pi

### 2 Responses

1. I noticed that in your videos, all your examples had negatives. My question is with more of a problem which looks like
64^3/4

• Okay, in that case put in in this format: x^y/z then go like this ^Z root( x^y). Without being able to type the the root thing it makes it really hard to say on this comment. But think of it this way, Something that is square rooted can also be written with an exponent on 1/2. The number on the bottom of the exponent is what the number’s root is and the number on top of the exponent is what goes inside the root.