Question

(2/3)^-2-(2 1/2)^-1+(-5/2)^-2

Answer 1

Объяснение:

$( \frac{2}{3} ) ^{ - 2} - {( 2\frac{1}{2}) }^{ - 1} + {( - \frac{5}{2}) }^{ - 2} = \frac{9}{4} - \frac{2}{5} - \frac{4}{25} = \frac{9}{4} - \frac{10 - 4}{25} = \frac{9}{4} - \frac{6}{25} = \frac{225 - 24}{100} = \frac{201}{100} = 2 \frac{1}{100} = 2.01$

Answer 2

To calculate the expression (2/3)^-2 - (2 1/2)^-1 + (-5/2)^-2, follow these steps:

1. Calculate each term individually:

   • (2/3)^-2: To raise a fraction to a negative exponent, take the reciprocal of the fraction and raise it to the positive exponent. So, (2/3)^-2 becomes (3/2)^2 = 9/4.
   • (2 1/2)^-1: Convert the mixed number to an improper fraction. 2 1/2 is equal to 5/2. Then, raise it to the power of -1, which means taking its reciprocal. So, (2 1/2)^-1 becomes 2/5.
   • (-5/2)^-2: To raise a negative fraction to a negative exponent, take the reciprocal of the fraction and raise it to the positive exponent. So, (-5/2)^-2 becomes (-2/5)^2 = 4/25.

2. Now, substitute the values back into the original expression: 9/4 - 2/5 + 4/25

3. To add and subtract these fractions, find a common denominator, which is 100. Rewrite each fraction with the common denominator: (9/4) * (25/25) - (2/5) * (20/20) + (4/25) * (4/4)

4. Perform the operations: (225/100) - (40/100) + (16/100)

5. Add and subtract the fractions: (225 - 40 + 16) / 100

6. Simplify the numerator: 201/100

So, the final result is 201/100, which can be further simplified to 2.01 when divided.