How do I solve exponential rules with the laws of exponents?

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I am trying to figure out how to solve exponential rules with the laws of exponents. I'm in a summer school Algebra 2B class and it was not explained very well. I have the laws in front of me with examples and I do not know how to conduct a solution when I work on a problem in the assignments. I have about five assignments to complete. If you could give me a shortcut or a memorizing explanation, that would be greatly appreciated. Thank you so much and please have a nice day.

Jun 29th, 2015

Thank you for the opportunity to help you with your question!

Law of Exponents

The exponents of a number is when how many times to use the number in multiplication.

8^3 =  8 X 8 X 8 = 512

In other words, 8^3  could be called “8 to the third power”, “8 to the power of 3”, or simply “8 cubed”


 8 is the base while 3 is the exponent or index

Another  example:  3^4 =  3 X 3 X 3 X 3 = 81

So an exponents saves use writing out lots of multiplies!

For example:  a ^7

  a^7 = a x a x a x a x a x a x a = aaaaaaaa

For example:  x^6 = xxxxxx

The Key to the Laws

 Writing all the letters down is the key to understanding the Laws.

Example:  x^2x^3 = (xx)(xxx) = xxxxx = x^5

The key to the law is just to remember  to write down all the letters ( as many as the exponents tells you to) and see if you can make sense of it.

The “Laws of Exponents  come from three ideas:

The exponent says how many times to use the number in multiplication

A negative exponent means divide because the opposite of multiplying is dividing

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 29th, 2015

Jun 29th, 2015
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