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

1 answer

First, let's simplify the innermost parentheses:

StartFraction 8 - ( -4 ) EndFraction = StartFraction 8 + 4 EndFraction = 12

Next, we'll evaluate the exponent:

(12)^3 = 12 × 12 × 12 = 1,728

Now let's simplify the fraction:

StartFraction 1,728 Over 5^2 - 8 × 2 EndFraction

StartFraction 1,728 Over 25 - 8 × 2 EndFraction = StartFraction 1,728 Over 25 - 16 EndFraction

Next, let's calculate the values:

StartFraction 1,728 Over 25 - 16 EndFraction = StartFraction 1,728 Over 25 -16 EndFraction = StartFraction 1,728 - 400 Over 25 EndFraction = StartFraction 1,328 Over 25 EndFraction

Finally, let's square this fraction:

StartFraction 1,328 Over 25 EndFraction^2 = StartFraction 1,328^2 Over 25^2 EndFraction = StartFraction 1,764,384 Over 625 EndFraction

The simplified expression is 1,764,384/625.