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Adding Exponents



When multiplying numbers in exponent notation with the same base, we can add the exponents.

Consider:

Text Box: a2 × a3 = (a × a) × (a × a × a)  = a2+3  = a5

This is the first law of exponents:

Text Box: am × an = am+ n

Example:

Simplify the following; give your answers in exponent form

Text Box: a)	33 × 32  b)	x5 × x3  c)

Solution:

Text Box: a)	33 × 32 = 33 + 2    	= 35    b)	x5 × x3 = x5 + 3  = x8    c)

Common Error : The first law of exponents does NOT apply to addition of numbers in exponent notation.

Text Box: am + an   am+ n

 

The following video shows some examples of adding exponents.



 

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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