SOLUTION: Describe two laws of exponents and provide an example illustrating each law.

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Question 126172: Describe two laws of exponents and provide an example illustrating each law.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Exponent Law # 1:


Let's say you have the expression 2%5Ex. Now, if you want to square this entire expression, you would simply say


%282%5E3%29%5E2


To go even further, you can use an exponent law that states: %28x%5Ey%29%5Ez=x%5E%28y%2Az%29
In other words, when you have 2 exponents (ie one exponent is raised to another exponent), you simply multiply the two exponents and that product will become the new exponent.

%282%5E3%29%5E2 Start with the given expression


2%5E%283%2A2%29 Use the previous identity %28x%5Ey%29%5Ez=x%5E%28y%2Az%29 to rewrite the expression. So we're simply going to multiply the exponents 3 and 2


2%5E%286%29 Multiply


64 Now raise 2 to the 6th power to get 64


So what we've shown is that %282%5E3%29%5E2=64



Notice how 2%5E3=8. So %282%5E3%29%5E2=8%5E2=64




So this example illustrates and supports the identity %28x%5Ey%29%5Ez=x%5E%28y%2Az%29


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Exponent Law # 2:


Now let's say you have the expression

x%5E2


and you want to multiply that by x%5E3


One way you could do it is simply note that x%5E2=x%2Ax and x%5E3=x%2Ax%2Ax

When you multiply x%5E2 and x%5E3, you get x%5E2%2Ax%5E3=%28x%2Ax%29%2A%28x%2Ax%2Ax%29=x%2Ax%2Ax%2Ax%2Ax=x%5E5



OR


You can use the identity x%5Ey%2Ax%5Ez=x%5E%28y%2Bz%29


This identity basically says that if you multiply two expressions that have the same base, you can simply add the two exponents


So in our case

x%5E2%2Ax%5E3=x%5E%282%2B3%29=x%5E5