Question - Solving a Mathematical Expression Involving Fractions and Exponents
Solution:
To solve the expression given in the image, we follow these steps:First, simplify the expression inside the parentheses:\[\left(\sqrt{\frac{4}{25}} - 1\right)\]Since the square root of a fraction is the square root of the numerator divided by the square root of the denominator, we have:\[\sqrt{\frac{4}{25}} = \frac{\sqrt{4}}{\sqrt{25}} = \frac{2}{5}\]Now, replace the square root with its simplified form in the original expression:\[\left(\frac{2}{5} - 1\right)\]To subtract 1 (which is the same as 5/5) from 2/5, we express 1 with a common denominator:\[\left(\frac{2}{5} - \frac{5}{5}\right)\]Now subtract the numerators while keeping the common denominator:\[\frac{2 - 5}{5} = \frac{-3}{5}\]Finally, raise this fraction to the power of 3:\[\left(\frac{-3}{5}\right)^3 = \frac{-3^3}{5^3} = \frac{-27}{125}\]So, the solution to the expression is $$-\frac{27}{125}$$.
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