Evaluate the following expression.(Type an integer or a simplified fraction.)
left parenthesis StartFraction 1 minus left parenthesis negative 4 right parenthesis cubed Over 5 squared minus 4 times 3 EndFraction right parenthesis squared
Let's evaluate the expression step by step.
First, let's simplify the expression inside the parentheses:
1 - (-4) = 1 + 4 = 5
Next, let's simplify the fraction:
[(5)^3] /(5^2 - 4*3) = 125/(25 - 12) = 125/13
Finally, let's square the fraction:
(125/13)^2 = (125^2) / (13^2) = 15625/169
Therefore, the simplified expression is 15625/169.
no
Apologies for the confusion. Let's evaluate the expression again step by step.
First, let's simplify the expression inside the parentheses:
1 - (-4) = 1 + 4 = 5
Next, let's calculate the square of 5:
5 squared = 5^2 = 25
After that, let's determine the result of multiplying 4 and 3:
4 times 3 = 4 * 3 = 12
Now, let's simplify the fraction inside the parentheses:
(1 - (-4)^3) / (25 - 12) = (1 - (-64)) / (25 - 12) = (1 + 64) / (25 - 12) = 65 / 13
Lastly, let's calculate the square of 65/13:
(65/13) squared = (65^2) / (13^2) = 4225/169
Therefore, the simplified expression is 4225/169.
To evaluate this expression, let's simplify each part step-by-step.
First, let's simplify the numerator of the fraction:
1 - ( -4 ) = 1 + 4 = 5
Next, let's simplify the denominator of the fraction:
5² = 5 × 5 = 25
Now, we can simplify the fraction:
(5³) / 25 = 5 × 5 × 5 / 25 = 125 / 25 = 5
Moving on to the rest of the expression:
4 × 3 = 12
Now, we can rewrite the expression using the simplified values:
(5 - 12)² = (-7)² = 49
Therefore, the evaluation of the given expression is 49.