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Chapter 0: Problem 124

Explain the quotient rule for exponents. Use \(\frac{5^{8}}{5^{2}}\) in your explanation.

Short Answer

Expert verified
The result of \(\frac{5^{8}}{5^{2}}\) applying the quotient rule for exponents is \(5^{6}\).

Step by step solution

01

Identify the Like Bases and Exponents

Begin by identifying the like bases and their exponents. In this case, the like base is \(5\) and the exponents are \(8\) and \(2\) for the numerator and the denominator respectively.
02

Apply the Quotient Rule

Now that we have identified the like bases and their exponents, apply the quotient rule, which states that when dividing like bases, keep the base and subtract the exponents. We keep the base as \(5\) and subtract the exponent of the denominator \(2\) from the exponent of the numerator \(8\), that is \(8-2 = 6\). This gives \(5^{6}\).
03

Simplify If Needed

The obtained expression \(5^{6}\) cannot be simplified further. We have now obtained the result using the quotient rule for exponents.

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