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Adding Exponents


What happens when numbers with exponents are multiplied?

Related Topics:
Introduction to Exponents
Rules of Exponents
Using Exponent Rules


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.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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