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

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