Answer:
[tex]\large\boxed{\left(25^{-\frac{3}{2}}\right)^\frac{1}{3}=\dfrac{1}{5}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ (a^n)^m=a^{nm}\\\\\left(25^{-\frac{3}{2}}\right)^\frac{1}{3}=25^{-\frac{3}{2}\cdot\frac{1}{3}}=25^{-\frac{1}{2}}\\\\\text{Use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{25^\frac{1}{2}}\\\\\text{Use}\ a^\frac{1}{n}=\sqrt[n]{a}\to a^\frac{1}{2}=\sqrt[2]{a}=\sqrt{a}\\\\=\dfrac{1}{\sqrt{25}}=\dfrac{1}{5}[/tex]
Following are the calculation to the given expression:
Given:
[tex] \to (25^{-\frac{3}{2})^{\frac{1}{3}} [/tex]
To find:
evaluate expression=?
Solution:
[tex]\to (25^{-\frac{3}{2})^{\frac{1}{3}}= ((5^2)^{-\frac{3}{2})^{\frac{1}{3}}\\ [/tex]
[tex]= (5^{2 \times -\frac{3}{2}})^{\frac{1}{3}}\\\\ = (5^{-3})^{\frac{1}{3}}\\ \\ = 5^{{-3}\times \frac{1}{3}}\\ \\ = 5^{-1}\\\\ =\frac{1}{5}[/tex]
The final answer is "[tex]{\frac{1}{5}}[/tex]".
Learn more:
brainly.com/question/8061466
