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Chapter 5: Problem 7

Rewrite \(\sqrt{a^{5}}\) using a single index.

Short Answer

Expert verified
Question: Rewrite the expression √(a^5) using a single index. Answer: a^(5/2)

Step by step solution

01

Identify the terms inside the square root

We start by recognizing the terms inside the square root, which are \(a^{5}\).
02

Apply the square root rule

Next, we apply the rule for square roots: \(\sqrt[n]{a^m}=a^{\frac{m}{n}}\). In our case, the expression is \(\sqrt{a^{5}}\) which implies n=2.
03

Rewrite using a single index

Therefore, we can rewrite \(\sqrt{a^{5}}\) as follows: $$ \sqrt{a^{5}}=a^{\frac{5}{2}} $$ The expression \(\sqrt{a^{5}}\) has been rewritten using a single index as \(a^{\frac{5}{2}}\).

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