Solving a Mathematical Expression Involving Fractions and Exponents
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 \(-\frac{27}{125}\).
