Evaluating the Expression: 5/9 + 1/2x(2/3)^3
In this article, we will evaluate the expression 5/9 + 1/2x(2/3)^3 and simplify it to its most reduced form.
Step 1: Evaluate the Exponentiation
First, let's evaluate the exponentiation part of the expression, which is (2/3)^3. To do this, we need to raise 2/3 to the power of 3.
(2/3)^3 = (2/3) × (2/3) × (2/3) = 8/27
Step 2: Multiply the Fraction by x
Next, we need to multiply the result by x, which gives us:
1/2x(8/27) = 4x/27
Step 3: Add the Two Fractions
Now, we need to add the two fractions 5/9 and 4x/27.
5/9 + 4x/27
To add these fractions, we need to find the least common multiple (LCM) of 9 and 27, which is 27. So, we can rewrite the fractions with the LCM as the denominator:
5/9 = 15/27 4x/27 = 4x/27
Now, we can add the two fractions:
15/27 + 4x/27 = (15 + 4x)/27
Final Result
Therefore, the final result of the expression 5/9 + 1/2x(2/3)^3 is:
(15 + 4x)/27
This is the simplified form of the expression.
