Question

Сравните: 1) (0,7)^20 и (-0,7)^20 2) -6,4^4 и (-6,4)^4 3) (-2,1)^19 и 2,1^19 4) (-0,2)^15 и -0,2^15

Answer 1

1) (0,7)^20 > (-0,7)^20  

2) -6,4^4 ≤  (-6,4)^4

3) (-2,1)^19  < 2,1^19

4) (-0,2)^15 ≤ -0,2^15

Answer 2

To compare the given expressions, we need to calculate the values of each expression. Let's go through each comparison step by step:

1. (0.7)^20 and (-0.7)^20: (0.7)^20 ≈ 0.00079792266 (-0.7)^20 ≈ 0.00079792266

Both expressions have the same positive value since an even exponent cancels out the negative sign. So, (0.7)^20 and (-0.7)^20 are approximately equal.

2. -6.4^4 and (-6.4)^4: -6.4^4 ≈ -1076.78 (-6.4)^4 ≈ 1076.78

Here, the negative sign in front of -6.4^4 makes the result negative. However, (-6.4)^4 is the same as 6.4^4 but with a positive sign since an even exponent preserves the positive value. So, -6.4^4 and (-6.4)^4 have the same magnitude but opposite signs.

3. (-2.1)^19 and 2.1^19: (-2.1)^19 ≈ -91.42697786 2.1^19 ≈ 91.42697786

Similar to the previous comparison, the negative sign in front of (-2.1)^19 changes the sign of the result. However, 2.1^19 is positive since an odd exponent preserves the original sign. So, (-2.1)^19 and 2.1^19 have the same magnitude but opposite signs.

4. (-0.2)^15 and -0.2^15: (-0.2)^15 ≈ -0.00032768 -0.2^15 ≈ -0.00032768

Both expressions are the same since an odd exponent preserves the negative sign. So, (-0.2)^15 and -0.2^15 are equal.

In summary:

1. (0.7)^20 and (-0.7)^20 are approximately equal.
2. -6.4^4 and (-6.4)^4 have the same magnitude but opposite signs.
3. (-2.1)^19 and 2.1^19 have the same magnitude but opposite signs.
4. (-0.2)^15 and -0.2^15 are equal.