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Chapter 5: Problem 92

Explain how to simplify an expression that involves a quotient raised to a power. Provide an example with your explanation.

Short Answer

Expert verified
A quotient raised to a power can be simplified by applying the power individually to the numerator and the denominator, then simplifying the resulting expression if possible. For example, \((\frac{2}{3})^4\) simplifies to \(\frac{16}{81}\).

Step by step solution

01

Understand the exponent rules

The fundamental rule to note here is that when you have a quotient raised to a power, the exponent applies to both the numerator and the denominator of the fraction. For example, if we have \((\frac{a}{b})^n\), it can be rewritten as \(\frac{a^n}{b^n}\).
02

Provide an Example

Let's consider an example where we simplify \((\frac{2}{3})^4\). Using the rule from step 1, this would be the same as \(\frac{2^4}{3^4}\) or \(\frac{16}{81}\).
03

Final Simplification

Looking at our example, \(\frac{16}{81}\) cannot be simplified any further, so this would be the final answer. If the numerator and denominator had common factors, you would have to simplify those as well. By consistently applying exponent rules, you can simplify expressions involving quotients raised to powers.

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