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Multiplication and Division Properties of Exponents - Problem 2

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Simplify a base with an exponent being raised to another power by multiplying the two exponents and leave the base the same. Simplify a fraction where the numerator and the denominator have the same based on subtracting the bottom exponent from the top. Leave the base the same.

Here I have a problem having to do with exponents and it also has variables in the base. So in order to solve it you could try to memorize the properties of exponents and hope that you get them right in you brain or if you want to get them right, you guys just write it out.

For example, x to the third means x times itself 3 times. There it is and then I need to write that twice. So here it comes again. Now I have x to the 3rd squared and I need to multiply that by 4 more Xs. So yeah it took me a while to write that all out but now I know I’m going to get the write answer. It’s going to be x to the 1, 2, 3, 4, 5, 6, 7, 8, 9, 10th, x to the 10th power. It’s still pretty easy to do and I’m pretty darn sure I’m going to get them all correct if I write it out.

Look at this one, same idea. You might have memorized the properties of how this division problems work or you can just write it out. X/x becomes one, so I’m left with just one x in my numerator or x to the first. You would have got that same answer if you knew to do x the 3rd take away 2, 3 take away 2. That would also give you x to the 1st power. So you guys, again I’ve said this before. You could try to memorize all those properties of exponents but you’re probably going to get them confused in your brain. Just write it out and every time you’ll get them correct and you can get an A+ on your exponents test.

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