Question

(-0,5)^-4 - 625^0,25 - (2 1\4)^-1 1\2

Answer 1

$-1/2 ^{-4} - 625^{1/4} - 9/4^{-3/2} = -2^{4} - \sqrt[4]{625} - \sqrt{( \frac {4}{9})^3 }$
$16-5- \sqrt\frac{256}{729} = 11- \frac{16}{27}= 10 \frac{11}{27}$

Answer 2

Let's break this expression down step by step:

(-0.5)^-4:

To raise a negative number to an even power, like -4, results in a positive number. Thus, we have:

(-0.5)^-4 = (1/(-0.5))^4 = (-2)^4 = 16

625^0.25:

To take the fourth root of 625, we can raise it to the power of 1/4. Thus, we have:

625^0.25 = (625^(1/4)) = 5

(2 1/4)^-1 1/2:

First, we need to convert the mixed number 2 1/4 to an improper fraction:

2 1/4 = (8/4) + (1/4) = 9/4

Next, we can use the power of a fraction rule, which says that (a/b)^c = a^c / b^c. Thus, we have:

(9/4)^(-1/2) = 1 / (9/4)^(1/2) = 1 / (√9 / √4) = 1 / (3/2) = 2/3

Now, we can substitute these values back into the original expression:

(-0.5)^-4 - 625^0.25 - (2 1/4)^-1 1/2 = 16 - 5 - 2/3 = 47/3

Therefore, the final answer is 47/3.