Calculation: the 1006th power of 9 * the 2013 power of (- 1 / 3) is equal to

Calculation: the 1006th power of 9 * the 2013 power of (- 1 / 3) is equal to

=(3^2)^1006*（-1/3）^2013
=3^2012*(-1/3)^2012*(-1/3)
=1*(-1/3)
=-1/3

Calculate the 2013 power of (- 2) and the 2014 power of (1-2) =? Detailed process

0

(- 2 / 3 2013) times (1.5's 2014 power),

 
 

The third power of a + B is calculated by the complete square formula and the square difference formula

(a+b)³
=(a+b)(a+b)²
=(a+b)(a²+2ab+b²)
=a³+3a²b+3ab²+b³

Use the square difference formula or complete square formula to calculate (2 + 1) (2? 2 + 1) (the fourth power of 2 + 1) (32nd power of 2 + 1) + 1 As the title

(2 + 1) (2? 2 + 1) (the fourth power of 2 + 1) (32nd power of 2 + 1) + 1
=(2-1) (2 + 1) (2? 2 + 1) (the fourth power of 2 + 1) (32nd power of 2 + 1) + 1
=The 64th power of 2 - 1 + 1 = the 64th power of 2

Using the square difference formula to calculate (A-1) (the fourth power of a + 1) (the second power of a + 1) (a + 1)

(A-1) (a + 1) is equal to (A's quadratic-1) (A's quadratic-1) (A's quadratic + 1) is equal to (A's fourth power-1)
(A's fourth power-1) (A's fourth power + 1) is equal to a's eighth power-1

Calculate the square of 999 with the square difference formula

999*999=(1000-1)*(1000-1)=1000*1000+1*1-2*1000=998001~
The man on the first floor is really NB. He is still a level 6 wizard

The square difference formula can also be used in reverse, that is, the square of a minus the square of B = (a-b) (B-A) (1 minus 1 / 2 of the square) (1 minus 1 / 3 of the square) (1 minus 1 / 4 of the square) (1 minus one square of 2009) (1 minus one square of 2010)

The original formula = (1 + 1 / 2) (1-1 / 2) (1 + 1 / 3) (1-1 / 3) (1+1/2010)(1-1/2010)=[(3/2)x(4/3)x(5/4)x…… x(2011/2010)]x[(1/2)x(2/3)x(3/4)x…… X (2009 / 2010)] = (2011 / 2) x (1 / 2010) = 2011 / 4020 note: the second line is to multiply the addition factor in brackets to one

(a + 2) (a ^ 2 + 4) (a ^ 4 + 16) (A-2), which is calculated by the square difference formula, is followed by the square

（a+2)(a^2+4)(a^4+16)(a-2)
=(a-2)（a+2)(a^2+4)(a^4+16）
=（a²-4)(a²+4)(a^4+16)
=(a^4-16)(a^4+16)
=a^8-256

Please use the square difference formula to calculate (3 + 2) (3 ﹣ 2 ﹣ 2) (the fourth power of 3 + the fourth power of 2) (the eighth power of 3 + the eighth power of 2)

This problem is too boring, the number is huge