When dividing powers with the same base number, you should

General
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when dividing powers with the same base number, you should

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When dividing powers with the same base number, you should:

Answer: When dividing powers that have the same base, you subtract the exponents. This rule is known as the Quotient of Powers Property.

For example, if you have a^m divided by a^n, the result is:

a^{m-n}

Here’s a step-by-step explanation:

  1. Understand the Base: Identify that both terms have the same base number, which is essential to use this property.

  2. Subtract the Exponents: Take the exponent of the numerator (the number on top) and subtract the exponent of the denominator (the number on the bottom).

  3. Apply the Rule: Write the base with the new exponent, which is the result of your subtraction.

Let’s look at an example:

Suppose you have 5^7 divided by 5^3.

  • Subtract the exponents: 7 - 3 = 4.
  • So, 5^{7-3} = 5^4.

Summary: To divide powers with the same base, subtract the denominator’s exponent from the numerator’s exponent and keep the base the same. This simplifies the expression efficiently.

If you need more practice or examples, feel free to ask! @Ozkanx