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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 expression \(\frac{5^{8}}{5^{2}}\) simplifies to \(5^{6}\) using the quotient rule for exponents.

Step by step solution

01

Identify the base and exponents

You can see that both terms in the expression have the same base, which is 5, and their exponents are 8 and 2. So, you have \(5^{8}\) divided by \(5^{2}\).
02

Apply the Quotient Rule

The quotient rule of exponent states: to divide numbers with the same base, subtract the exponent of the denominator from the exponent of the numerator. So, you subtract the exponent 2 from 8, which gives you \(5^{(8-2)}\).
03

Simplify

Finally, simplify \(5^{(8-2)}\) to get \(5^{6}\). Now the expression \(\frac{5^{8}}{5^{2}}\) has been simplified to \(5^{6}\) using the quotient rule for exponents.

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