The 11 th power of 31 is compared with the 14 th power of 17

The 11 th power of 31 is compared with the 14 th power of 17

The 14th power of 17 is equal to the 11th power of 17 times the 3rd power of 17

The 14th power of 17 and the 11th power of 31, patience, please 1.17^14>16^14=(2^4)^14=2^56 31 ^ 1131 ^ 11 (^ is the power --) Why can the power of 16 ^ 14 be compared with that of 32 ^ 11? One of them is bigger and the other is smaller? 2.17^14=1.68×10^17 31^11=2.54×10^16 Why 2.54 and 1.68?

Because 16 ^ 14 > 32 ^ 11, 17 ^ 14 is larger than the larger number, and 31 ^ 11 is smaller than the smaller number, then 17 ^ 14 > 31 ^ 11 must be obtained
The second should be experience or calculation

Given that the a power of 2 = 3, the B power of 2 = 6, and the C power of 2 = 12, the quantitative relationship between a, B, C, try to compare the size of the 14 th power of 17 and the 11 th power of 31

17^14>16^14=2^56>2^55=32^11>31^11
2^a = 3 2^b = 6 2^c = 12
2^b * 2^b = 6 * 6 =36
2^a * 2^c = 3 * 12 =36
2^(2b)=2^(a+c)

Compare the size of the following two groups: (1) the third power of 2 + radical 7 and 4: (2) Radix 7 + Radix 10 and Radix 3 + Radix 14

（1）
2＋√7³＝2＋√343； 4＝√16；
∵√343＞√16
∴2＋√7³＞4；
I don't know if my formula is in line with your written expression;
（2）
﹙√7＋√10﹚²＝17＋2√70；
﹙√3＋√14﹚²＝17＋2√42；
∵70＞42；
∴√7＋√10＞√3＋√14；

Compare three numbers: root 2, 2 / 3 of the negative first power, the third with the sign under the size of the relationship The result is: radical 2

Let a = radical 2
B = three times with the sign
Then the sixth power of a = 2 3 = 8
The sixth power of B = 3? = 9
Eight

Square root 2, root 3, square root 6, how do these three numbers compare?

The square of each square root of 6 is:
8、9、6
So the square root 3 is greater than the root 2 is greater than the root 6 to the sixth power

if A − B − 3 and | a + B + 1 | are opposite numbers to each other. What is the value of (a + b) 5?

A kind of
A − B − 3 and | a + B + 1 | are opposite numbers to each other,
Qi
a−b−3+|a+b+1|＝0．
A kind of
A − B − 3 ≥ 0 and | a + B + 1 | ≥ 0,
A-b-3 = 0 and a + B + 1 = 0
A = 1, B = - 2
∴（a+b）5=（1-2）5=（-1）5=-1．

Compare the a + 2 / 3 power of 0.9 with (a + 1) (a + 2) power under the root sign of 0.9

We can only compare the size of a + 2 / 3 and (a + 1) (a + 2) under the root sign. First of all, we discuss the value of a, because the root must be meaningful. Then (a + 1) and (a + 2) are the same sign. When both are greater than 0, a is greater than or equal to - 1, and when they are less than 0, a is less than or equal to - 2

(sin square 65 degrees cos square 65 degrees) / (sin square 65 degrees cos square 65 degrees)

(sin square 65 degrees cos square 65 degrees) / (sin square 65 degrees cos square 65 degrees)
=(sin square 65 degrees + cos square 65 degrees) (sin square 65 degrees - cos square 65 degrees)
/(sin square 65 degrees - cos square 65 degrees)
=Sin square 65 degrees + cos square 65 degrees
=1.

Tan α = 3 find sin squared α - sin α cos α + 1

Sin squared α - sin α cos α + 1
tanα=3=3/1
=（3√10/10）/（√10/10）
=|sina|/|cosa|
Sin squared α - sin α cos α + 1 = 1 / 10-3 / 10 + 1 = 4 / 5