Evaluate the following expression.
left parenthesis StartFraction 1 minus left parenthesis negative 4 right parenthesis cubed Over 5 squared minus 4 times 3 EndFraction right parenthesis squared
To evaluate the given expression, we start by simplifying the numerator of the fraction:
1 - (-4) = 1 + 4 = 5
Next, we simplify the denominator of the fraction:
5^2 - 4 * 3 = 25 - 12 = 13
So, the fraction becomes 5/13.
The expression now becomes:
(5/13)^2 = (5/13) * (5/13) = 25/169
Therefore, the evaluated expression is 25/169.
To evaluate the given expression step-by-step, let's simplify it:
1. Inside the parentheses, first evaluate the expression (1 - (-4))^3.
This simplifies to (1 + 4)^3 = 5^3 = 125.
2. Next, evaluate the expression (5^2 - 4 × 3)^2.
Simplifying further, we have (25 - 12)^2 = 13^2 = 169.
3. Finally, evaluate the expression 125 / 169.
The simplified value is approximately 0.7396.