I posted this problem the other day and someone answered it but when I checked my book I realized that I wrote the problem wrong. This morning when I posted I had put the wrong answer. The answer is suppose to be 1/8 but I don't understand how to solve the problem. Help would be greatly appreciated.
(1/4)^2/(1/2-3/4)+ 3/2^3 (It's all one equation)
First of all, it is not an equation, since it does not have an equal sign. Second, I think you wanted the sequence to be like this, so it is not just the 2 that is cubed:
(1/4)^2/(1/2-3/4)+ (3/2)^3
(3/2)^3 = 3/2 * 3/2 * 3/2 = 27/8
(1/4)^2 = 1/4 * 1/4 = 1/16
1/2 - 3/4 = -1/4
(1/16)/(-1/4) = (1/16) * -4 = -4/16 = -1/4 = -2/8
-2/8 + 27/8 = 25/8 = 3 1/8
I hope this breaks it down well enough for you to understand.
To solve this equation, let's break it down step by step:
Step 1: Simplify the expression inside the parentheses.
The expression inside the parentheses is (1/4)^2 / (1/2 - 3/4).
First, let's simplify (1/4)^2. When you raise a fraction to a power, you raise the numerator and denominator to that power. So, (1/4)^2 becomes (1^2)/(4^2) or 1/16.
Next, let's simplify (1/2 - 3/4). Here, we need a common denominator, which is 4. We can rewrite 1/2 with a denominator of 4, getting 2/4. So, (1/2 - 3/4) becomes (2/4 - 3/4) or -1/4.
Therefore, the expression inside the parentheses simplifies to 1/16 / (-1/4).
Step 2: Simplify the division fraction.
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So, we can rewrite 1/16 / (-1/4) as 1/16 * (-4/1).
Multiplying the numerators (1 * -4) gives you -4, and multiplying the denominators (16 * 1) gives you 16.
Therefore, the expression inside the parentheses simplifies to -4/16 or -1/4.
Step 3: Simplify the next part of the equation.
The next part of the equation is 3/2^3.
First, let's simplify 2^3, which is 2 raised to the power of 3. This equals 2 * 2 * 2, which is 8.
Therefore, 3/2^3 simplifies to 3/8.
Step 4: Combine the simplified expressions.
Now that we have simplified both parts of the equation, we can combine them.
The equation becomes (-1/4) + 3/8.
To add fractions with different denominators, we need to find a common denominator. The least common multiple of 4 and 8 is 8. So, we can rewrite the fractions with a common denominator:
(-1/4) + 3/8 becomes (-2/8) + 3/8.
Now, we can add the numerators: (-2 + 3) gives us 1.
Therefore, the equation becomes 1/8, which is equal to the answer you mentioned: 1/8.