Evaluate the following expression.
{5-(-3)³}²
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6²-7*4
To evaluate the expression, we will first simplify the numerator and denominator separately.
Numerator:
{5-(-3)³}²
Inside the parentheses, we have (-3)³. This means we need to cube -3.
(-3)³ = -3 * -3 * -3 = -27
Substituting this value back into the expression, we have {5-(-27)}².
Now let's simplify the expression inside the curly brackets.
5 - (-27) = 5 + 27 = 32
Substituting this value back into the expression, we have 32².
32² = 32 * 32 = 1024
So the numerator simplifies to 1024.
Denominator:
6² - 7 * 4
6² = 6 * 6 = 36
Now let's simplify the multiplication.
7 * 4 = 28
The denominator simplifies to 36 - 28 = 8.
Now we can substitute the simplified values back into the original expression.
Numerator: 1024
Denominator: 8
The final expression is:
1024/8
Dividing 1024 by 8 gives us a result of 128.
Therefore, the evaluated expression is equal to 128.
To evaluate the expression, let's break it down step by step.
Step 1: Evaluate the expression within the first set of braces: 5 - (-3)³.
To do this, we need to start with the exponent.
(-3)³ means -3 raised to the power of 3. Since the base is negative, the result will also be negative. (-3)³ = -3 * -3 * -3 = -27.
So, the expression becomes: 5 - (-27) = 5 + 27 = 32.
Step 2: Evaluate the expression within the second set of braces: 32².
To do this, we need to square 32.
32² = 32 * 32 = 1024.
So, the expression becomes: 1024.
Step 3: Evaluate the expression in the denominator: 6² - 7 * 4.
To do this, start with 6² which means 6 * 6 = 36.
Next, multiply 7 by 4: 7 * 4 = 28.
So, the expression becomes: 36 - 28 = 8.
Step 4: Divide the evaluated expression from step 2 by the evaluated expression from step 3: 1024 / 8.
To do this, simply divide 1024 by 8.
1024 / 8 = 128.
So, the value of the given expression is 128.