Simplify $\left(\frac{3}{5}\right)^2$
Answer (1)
To simplify the expression, square both the numerator and the denominator of the fraction.
Calculate 3 2 = 9 .
Calculate 5 2 = 25 .
The simplified expression is 25 9 .
Explanation
Understanding the Problem We are asked to simplify the expression ( 5 3 ) 2 . This means we need to square the fraction 5 3 .
Squaring a Fraction To square a fraction, we square both the numerator and the denominator separately. That is, ( b a ) 2 = b 2 a 2 .
Calculating Squares In our case, we have a = 3 and b = 5 . So we need to calculate 3 2 and 5 2 .
3 2 = 3 × 3 = 9
5 2 = 5 × 5 = 25
Final Result Therefore, ( 5 3 ) 2 = 5 2 3 2 = 25 9 .
Examples
Fractions and exponents are useful in many real-world situations. For example, if you are scaling a recipe by a factor of 5 3 , and the original recipe calls for 1 cup of flour, you would need ( 5 3 ) × 1 = 5 3 cups of flour. If you are calculating the area of a square with side length 5 3 meters, the area would be ( 5 3 ) 2 = 25 9 square meters. These concepts are also used in calculating probabilities and proportions.
