Subjects algebra

Negative Fractional Exponent 7Bfaea

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Negative Fractional Exponent 7Bfaea


1. The problem is to simplify or understand the expression $\left(x^2+5\right)^{-\frac{1}{4}}$. 2. The expression has a negative fractional exponent. Recall the rule: $a^{-n} = \frac{1}{a^n}$ and $a^{\frac{m}{n}} = \sqrt[n]{a^m}$. 3. Applying the negative exponent rule, we rewrite: $$\left(x^2+5\right)^{-\frac{1}{4}} = \frac{1}{\left(x^2+5\right)^{\frac{1}{4}}}$$ 4. The fractional exponent $\frac{1}{4}$ means the fourth root, so: $$\frac{1}{\left(x^2+5\right)^{\frac{1}{4}}} = \frac{1}{\sqrt[4]{x^2+5}}$$ 5. Therefore, the expression represents the reciprocal of the fourth root of $x^2+5$. This is the simplified form and interpretation of the given expression.