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Chapter 5: Problem 5

Write \(\frac{1}{x^{-1 / 2}}\) using a positive index.

Short Answer

Expert verified
Question: Rewrite the expression with a positive exponent: \(\frac{1}{x^{-1/2}}\) Answer: \(x^{1/2}\)

Step by step solution

01

Identify the negative exponent

In the given expression, \(\frac{1}{x^{-1/2}}\), the negative exponent is \(-1/2\). Step 2: Apply the rule for negative exponents
02

Apply the rule for negative exponents

We know that \(\frac{1}{x^{-n}} = x^n\). Here, \(n=-1/2\). So, applying this rule, we get: \(\frac{1}{x^{-1/2}} = x^{1/2}\). So, the expression with a positive index is:
03

Final Answer

\(\frac{1}{x^{-1 / 2}} = x^{1/2}\).

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