Simplifying expressions with exponents worksheet with answers

1. Which of the following is equivalent to the expression below?

2. Simplify the following expression using positive exponents.

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About This Quiz & Worksheet

Test your ability to simplify expressions using exponents in this quiz/worksheet combo. You will have five practice problems to solve, and you will need to know how to use the product of powers property and how to work with negative exponents.

Quiz & Worksheet Goals

To simplify the problems on this quiz correctly, you should be familiar with the following exponent properties:

• Quotient of powers
• Product of powers
• Power of a product

Skills Practiced

• Problem solving - use acquired knowledge to solve exponent practice problems
• Distinguishing differences - compare and contrast the functions of the exponent properties in the lesson
• Knowledge application - use your knowledge to answer questions about simplifying using positive exponents

Additional Learning

To view more examples, go to the lesson called How to Simplify Expressions with Exponents. This lesson also covers these objectives:

• Review all of the properties of exponents
• Learn the manual process of simplifying expressions using exponents
• Use positive exponents

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Purplemath

For this section in your textbook, and on the next test, you'll be facing at least a few highly complex simplification exercises. You may never again see anything so complicated as these, but they're not that difficult to do, as long as you're careful.

This is not a time to try to do three steps all at once in your head! But if you're methodical and neat, you should be able to get all the points.

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MathHelp.com

• Simplify the following expression:

Before I can cancel anything off, I need to simplify that top parentheses, because it has a negative exponent on it. I can't cancel off, say, the a's, because that a4 isn't really on top. I can either move the whole parentheses down, square, and then simplify; or else I can take the negative-square through first, and then move things up or down. I'll show both ways:

 moving the parentheses first: 

 squaring first: 

There are other ways to go about simplifying the above. As long as each step is logically valid and you get the right answer, your particular sequence of steps will have been correct.

• Simplify the following expression:

This is a special case. The negative exponent says that whatever is on top should go underneath, and whatever is underneath should go on top. So I'll just flip the fraction (remembering to change the power from a negative to a positive), and simplify from there:

Note: This "flipping the fraction" technique only works if the negative exponent is on the whole fraction.

• Simplify the following expression:

There are so many ways I can do this. I'll show four:

 Method A: flip inside, simplify, 
 do negative cube, flip, 
 and simplify: 

 Method B: flip inside, simplify, 
 flip the fraction, and cube: 

 Method C: flip the fraction, 
 simplify inside, cube, flip the 
 negative exponents, 
 and simplify: 

 Method D: flip the fraction, 
 flip the negative exponents, 
 simplify, and cube: 

You should expect to see at least one exercise on your test that is as complicated as this last example. While you may rarely, if ever, again see another exercise like this, developing the habits of care and organization necessary to complete these reliably will stand you in good stead for the rest of your career.

You can use the Mathway widget below to practice simplifying with exponents. Try the entered exercise, or type in your own exercise. Then click the button to compare your answer to Mathway's.

(Click "Tap to view steps" to be taken directly to the Mathway site for a paid upgrade.)

URL: https://www.purplemath.com/modules/simpexpo3.htm