What is 5 to the power of 3 divided by 5 to the power of 6?
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sqdancefan 6 months ago
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Answer:

  1/5³ = 1/125 = 5⁻³

Step-by-step explanation:

It can be useful to remember that an exponent signifies repeated multiplication.

  5^3 = 5×5×5

  5^6 = 5×5×5×5×5×5

Then the ratio is ...

 

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If you want to leave this in terms of exponents, you can see that factors in the denominator cancel (subtract from) those in the numerator. That is ...

 

The same sort of exponent arithmetic works to leave a numerator value with a negative exponent:

 

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Additional comment

These ideas are formulated as the rules of exponents:

  • (a^b)/(a^c) = a^(b-c)
  • 1/(a^b) = a^-b

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