\( \frac{1}{\left(x^{2}+2\right)^{-\frac{5}{3}}} \) Answer \( \frac{1}{\sqrt[3]{\left(x^{2}+2\right)^{5}}} \) \( \sqrt[3]{\left(x^{2}+2\right)^{5}} \)

Simplify the expression by following steps: - step0: Solution: \(\left(x^{2}+2\right)^{\frac{5}{3}}\) - step1: Simplify: \(x^{2}\sqrt[3]{\left(x^{2}+2\right)^{2}}+2\sqrt[3]{\left(x^{2}+2\right)^{2}}\) Calculate or simplify the expression \( 1/(x^2 + 2)^(-5/3) \). Simplify the expression by following steps: - step0: Solution: \(\frac{1}{\left(x^{2}+2\right)^{\frac{-5}{3}}}\) - step1: Rewrite the fraction: \(\frac{1}{\left(x^{2}+2\right)^{-\frac{5}{3}}}\) - step2: Express with a positive exponent: \(\frac{1}{\frac{1}{\left(x^{2}+2\right)^{\frac{5}{3}}}}\) - step3: Multiply by the reciprocal: \(1\times \left(x^{2}+2\right)^{\frac{5}{3}}\) - step4: Multiply: \(\left(x^{2}+2\right)^{\frac{5}{3}}\) - step5: Simplify: \(x^{2}\sqrt[3]{\left(x^{2}+2\right)^{2}}+2\sqrt[3]{\left(x^{2}+2\right)^{2}}\) Let's break down the expression \( \frac{1}{\left(x^{2}+2\right)^{-\frac{5}{3}}} \) step by step. 1. **Understanding the Expression**: The expression can be rewritten using the property of exponents: \[ \frac{1}{a^{-b}} = a^{b} \] Therefore, we have: \[ \frac{1}{\left(x^{2}+2\right)^{-\frac{5}{3}}} = \left(x^{2}+2\right)^{\frac{5}{3}} \] 2. **Final Form**: The expression \( \left(x^{2}+2\right)^{\frac{5}{3}} \) can also be expressed in radical form: \[ \left(x^{2}+2\right)^{\frac{5}{3}} = \sqrt[3]{\left(x^{2}+2\right)^{5}} \] Thus, we conclude that: \[ \frac{1}{\left(x^{2}+2\right)^{-\frac{5}{3}}} = \sqrt[3]{\left(x^{2}+2\right)^{5}} \] Both forms are equivalent, and the simplification confirms that the expression is indeed correct.