Given that m plus N is equal to 10 and Mn is equal to 24, evaluate 1, the second power of m plus the second power of N, and the second power of (M minus n)

1：m^2+n^2
=(m+n)^2-2mn
=100-48
=52
2：(m-n)^2
=m^2+n^2-2mn
=52-48
=4

The square of m plus m minus 1 equals 0. What is the third power of m plus 2 times the square of m plus 2004

Because m ^ 2 + M-1 = 0, m ^ 2 = 1-m
So m ^ 3 + 2m ^ 2 + 2004 = m ^ 2 (M + 2) + 2004 = (1-m) [(1 + m) + 1] + 2004 = 1-m ^ 2 + 1-m + 2004 = - (m ^ 2 + m-1) + 1 + 2004 = 2005

It is known that the power of 3M times the power of 9m times the power of 27m times the power of 81m M is the power! Given that 3M times 9m times 27m times 81m = 3 to the 30th power, find the value of M

3^m*9^m*27^m*81^m=3^30
3^(m+2m+3m+4m)=3^30
3^(10m)=3^30
10m=30
M=3

(2 / 3) is 2011 power * (3 / 2) is 2012 power * (- 1) is 2013 power Find the result of the above question,

(2 / 3) to the 2011 power * (3 / 2) to the 2012 power * (- 1) to the 2013 power
=The 2011 power of (2 / 3) * the 2011 power of (3 / 2) × the 2013 power of 3 / 2 * (- 1)
=(2 / 3 × 3 / 2) 2011 power × 3 / 2 * (- 1) 2013 power
=1×3/2×（-1）
=-3/2

It is known that: if | A-1 | and | B + 2 | are opposite to each other, find: (a + b) to the 2013 power - (a + b) to the 2012 power + (a + b) to the 2011 power and - (a + b) to the 2010 power + -The square of (a + b) + the value of (a + b)

It is known that if | A-1 | and | B + 2 | are opposite numbers to each other,
∴a-1=0;
a=1;
b+2=0;
b=-2;
∴a+b=1-2=-1;
The 2013 power of (a + b) - (a + b) is the 2012 power of (a + b) + (a + b) is the 2011 power of - (a + b) and the 2010 power of - (a + b) + -The square of (a + b) + the value of (a + b)
=-1-1-1-1-...-1
=-1×2013
=-2013;
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What is the first power of a plus the second power of a plus the third power of a plus the fourth power of a plus the fifth power of a

Equivalency sequence
S = a (the 5th power of 1-A) \ (1-A)

The result is obtained by calculating the 2005 power of (- 2) and the 2006 power of (- 2)

There are two methods. One is to divide the 2006 times of (- 2) into the times of (- 2) times the 2005 times of (- 2). The real formula becomes the 2005 times of (- 2) minus the 2005 times of two (- 2). Finally, there is a - 1 (- 2) 2005 times left. Because the odd power of negative numbers is negative, plus a negative sign, the result is the 2005 times of positive 2

The minus half power of 2 is equal to? How to calculate it?

To the minus half power of 2
=1 / (1 / 2 of 2)
=1/√2
=√2/2

The minus half power of 8 is equal to?

The minus half power of 8 is equal to √ 2 / 4

How to calculate the positive and negative power of a number?

If a ^ (n / M) = (a ^ n) ^ (1 / M), calculate a ^ n first, and then open the root of the result to the m power;
Negative number: for example, a ^ (- n) = 1 / (a ^ n)

Given that m plus N is equal to 10 and Mn is equal to 24, evaluate 1, the second power of m plus the second power of N, and the second power of (M minus n)