e. $$ \left[\left(\frac{5}{2}\right)^{\frac{1}{2}} \cdot\left(\frac{5}{2}\right)^{\frac{1}{3}}\right]^{\frac{6}{5}} \cdot \sqrt{\left(\frac{5}{2}\right)^{-1}}= $$

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UpStudy AI · Accepted Answer

Vamos a simplificar la expresión $$ \left[\left(\frac{5}{2}ight)^{\frac{1}{2}} \cdot\left(\frac{5}{2}ight)^{\frac{1}{3}}ight]^{\frac{6}{5}} \cdot \sqrt{\left(\frac{5}{2}ight)^{-1}} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\left(\frac{5}{2}ight)^{\frac{1}{2}}\left(\frac{5}{2}ight)^{\frac{1}{3}}ight)^{\frac{6}{5}}\sqrt{\left(\frac{5}{2}ight)^{-1}}$$
- step1: Multiply the numbers:
  $$\left(\frac{5^{\frac{5}{6}}}{2^{\frac{5}{6}}}ight)^{\frac{6}{5}}\sqrt{\left(\frac{5}{2}ight)^{-1}}$$
- step2: Simplify the root:
  $$\left(\frac{5^{\frac{5}{6}}}{2^{\frac{5}{6}}}ight)^{\frac{6}{5}}	imes \frac{\sqrt{10}}{5}$$
- step3: Evaluate the power:
  $$\frac{5}{2}	imes \frac{\sqrt{10}}{5}$$
- step4: Reduce the numbers:
  $$\frac{1}{2}\sqrt{10}$$
- step5: Multiply:
  $$\frac{\sqrt{10}}{2}$$
El resultado de la expresión es $$ \frac{\sqrt{10}}{2} $$.

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