# Use properties of exponents to write an equivalent expression

Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top rather than below a "1"but this is incorrect.

Remind the student that the exponent simply describes the number of factors of the base. And I mustn't try to subtract the numbers, because the 5 and the 3 in the fraction " " are not at all the same as the 5 and the 3 in rational expression " ".

Note: Do not allow the student to use a calculator on this task. Uses a contrived rule e.

### Equivalent expressions with exponents worksheet

But the basic reasoning is the same. Let's move on to expressions that are a bit more complex. Can you explain the work you did for this problem? I have three extra 6's, and they're on top. Simplify the following expression: I mustn't forget that the "5" and the "3" are just numbers. Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Questions Eliciting Thinking How do you know when to add exponents and when to multiply them?

Can you explain the work you did for this problem? For the variables, I have two extra copies of x on top, so the answer is: Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing.

How many extra copies of 5 do I have, and where are they? What does an exponent mean? What rule or strategy did you use to find equivalent expressions?

## Use the properties of exponents to simplify the expression

Simplify the following expression: How many extra copies of t do I have, and where are they? Content Continues Below Simplify the following expression: This question is a bit different, because the larger exponent is on the term in the denominator. Provide similar examples as explanations of other exponent properties using both positive and negative exponents. Does not attempt to use any exponent properties but instead tries to do the actual calculations. Instructions for Implementing the Task This task can be implemented individually, with small groups, or with the whole class. Examples of Student Work at this Level The student: Uses the wrong integer exponent rule for the given situation. Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". The answers will start feeling fairly obvious to you. The teacher asks the student to complete the problems on the Equivalent Powers Expressions worksheet. The teacher asks follow-up questions, as needed. Instructional Implications Review the meaning of integer exponents and the properties of integer exponents. For the variables, I have two extra copies of x on top, so the answer is: Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing.

But let's suppose that I've forgotten the rules again.

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