Breaking Down (2/3)^2 (3x) - Step by Step

Welcome to our lesson on breaking down complex expressions!Let's examine this expression with a fraction squared multiplied by a term.We can break this expression into two main parts.To solve this correctly, we need to follow the order of operations.Since we have parentheses and an exponent, we'll focus on these first.Let's look more closely at the squared fraction.When we square a fraction, we multiply it by itself. The parentheses ensure we square both the numerator and denominator.Each part of the fraction plays a crucial role: the numerator two, the denominator three, and the exponent two.The parentheses are crucial here - they tell us to square the entire fraction, not just the numerator or denominator individually.Now that we've identified the parts and understand what the exponent means, we're ready to perform the actual calculations.To square a fraction, we need to multiply both the numerator and denominator by themselves.Let's start with the numerator. Two times two equals four.For the denominator, we multiply three times three, which equals nine.This gives us our simplified result of four ninths.A common mistake is to only square the numerator and leave the denominator unchanged.Remember this important rule: when squaring a fraction, you must square both the numerator and the denominator.Now that we have four ninths, we can move on to the next step.Now that we have simplified the squared fraction to four-ninths, we'll multiply it by three x.When multiplying a fraction by a term, we multiply the numerator by the entire term, keeping the denominator the same.This gives us twelve x over nine.Looking at our fraction, we can see that both twelve and nine are divisible by three.Dividing both the numerator and denominator by three simplifies our fraction.Our final simplified answer is four x over three.