Evaluate the following expression.
left parenthesis StartFraction 8 minus left parenthesis negative 4 right parenthesis cubed Over 5 squared minus 8 times 2 EndFraction right parenthesis squared
First, we need to simplify the expression inside the parentheses:
8 - (-4) = 8 + 4 = 12
Next, we solve the exponent:
12^3 = 12 * 12 * 12 = 1728
Now, we can simplify the expression further:
5^2 = 5 * 5 = 25
8 * 2 = 16
Now we can substitute these values back into the expression:
StartFraction 1728 Over 25 - 16 EndFraction^2
Next, we subtract 16 from 25:
25 - 16 = 9
Now we can substitute this value back into the expression:
StartFraction 1728 Over 9 EndFraction^2
Finally, we solve the remaining exponent:
(1728/9)^2 = (1728/9) * (1728/9) = 2985984/81 ≈ 36869.93
Therefore, the evaluated expression is approximately 36869.93.
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I apologize for the incorrect answer. Let's reevaluate the expression:
Start by simplifying the expression inside the parentheses:
8 - (-4) = 8 + 4 = 12
Next, solve the exponent:
12^3 = 12 * 12 * 12 = 1728
Now, we simplify the expression further:
5^2 = 5 * 5 = 25
8 * 2 = 16
Next, we substitute these values back into the expression:
StartFraction 1728 Over 25 - 16 EndFraction^2
Now, subtract 16 from 25:
25 - 16 = 9
Substitute this value back into the expression:
StartFraction 1728 Over 9 EndFraction^2
Finally, solve the remaining exponent:
(1728/9)^2 = (192)^2 = 36864
Therefore, the evaluated expression is 36864.
no no noooo
I apologize for the mistake. Let's reevaluate the expression:
First, simplify the expression inside the parentheses:
8 - (-4) = 8 + 4 = 12
Next, solve the exponent:
(-4)³ = (-4) * (-4) * (-4) = -64
Now, simplify the expression further:
5² = 5 * 5 = 25
8 * 2 = 16
Now, substitute these values back into the expression:
(12/25 - 16)²
Next, subtract 16 from 12/25:
12/25 - 16 = (12 - 16*25)/25 = (12 - 400)/25 = -388/25
Now, substitute this value back into the expression:
(-388/25)²
Finally, solve the remaining exponent:
(-388/25)² = (-388/25) * (-388/25) = 150544/625 = 240.8704
Therefore, the evaluated expression is approximately 240.8704.
To evaluate the given expression, let's simplify it step-by-step.
Step 1: Evaluate the expressions inside the parentheses.
⇒ 8 - ( -4 ) = 8 + 4 = 12
Step 2: Evaluate the numerator of the fraction.
⇒ (12^3) = 12 * 12 * 12 = 1,728
Step 3: Evaluate the denominator of the fraction.
⇒ 5^2 - 8 * 2 = 25 - 16 = 9
Step 4: Divide the numerator by the denominator.
⇒ 1,728 / 9 = 192
Step 5: Square the result.
⇒ (192)^2 = 192 * 192 = 36,864
Therefore, the value of the given expression is 36,864.
To evaluate the given expression, let's break it down step by step:
Step 1: Evaluate the exponent inside the parentheses:
Start by evaluating the expression inside the parentheses, which is (-4) cubed. To cube a number, we multiply it by itself twice: (-4) * (-4) * (-4) = -64.
Step 2: Evaluate the exponent outside the parentheses:
Next, evaluate the rest of the expression inside the parentheses. The expression is 8 - (-64), which simplifies to 8 + 64 = 72.
Step 3: Evaluate the numerator of the fraction:
Now, let's evaluate the numerator of the fraction. The numerator is (8 - (-4))^3, which simplifies to (8 + 4)^3 = 12^3 = 1728.
Step 4: Evaluate the denominator of the fraction:
The denominator of the fraction is (5^2 - 8 * 2). First, evaluate the multiplication: 8 * 2 = 16. Then, evaluate the exponent: 5^2 = 25. Finally, subtract 16 from 25: 25 - 16 = 9.
Step 5: Evaluate the fraction:
Now that we have the numerator (1728) and the denominator (9), we can express the fraction as a decimal by dividing the numerator by the denominator: 1728 / 9 = 192.
Step 6: Evaluate the squared expression:
Lastly, we square the result obtained in step 5, which is 192, by multiplying it by itself: 192 * 192 = 36,864.
Therefore, the value of the given expression is 36,864.