WAT IS 2/3 TO THE 2ND POWER TIMES 3/5 TO THE 2ND POWER
(2/3) * (2/3) = 4/9
(3/5) * (3/5) = 9/25
(4/9) * (9/25) = 36/225 = 4/25
To simplify the expression (2/3)^2 * (3/5)^2, you need to raise both fractions to the power of 2 and then multiply them together. Let's break it down step by step:
Step 1: Raise (2/3) to the power of 2.
To raise a fraction to the power, you raise both the numerator and denominator to that power. For (2/3)^2, you square the numerator and denominator individually:
(2/3)^2 = (2^2) / (3^2) = 4/9.
Step 2: Raise (3/5) to the power of 2.
Similarly, for (3/5)^2, you square the numerator and denominator:
(3/5)^2 = (3^2) / (5^2) = 9/25.
Step 3: Multiply the two results together.
Now, multiply the fractions (4/9) and (9/25):
(4/9) * (9/25) = (4 * 9) / (9 * 25) = 36/225.
Step 4: Simplify the result.
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and denominator, and divide both by it:
GCD(36, 225) = 9.
Therefore, divide both the numerator and denominator by 9:
36/225 = (36/9)/(225/9) = 4/25.
So, (2/3)^2 * (3/5)^2 simplifies to 4/25.