Сила натуральной степени

" People unfamiliar with algebra can not imagine the wonderful things that can be achieved with the help of ... called science."
G.W Leibniz

Determination of a natural indicator
Powers of a with natural exponent n is the product of n factors, each of which is equal to a.

Properties with a natural indicator of the degree of

Determination of the zero indicator
The degree of a, not equal to zero , with zero is equal to one

Multiplying powers with the same bases
For any number a and any positive integers m and n
Multiplying powers with the same bases of the base is left unchanged , and the figures add up

The division of powers with the same bases
For any
arbitrary natural
number
and m and n, such that m> n
When dividing powers with the same base bases are left unchanged , and the dividend is subtracted from the index index divider

Exponentiation works
For any numbers a and b and any positive integer n
With the construction of the power works erected in the degree of each factor and multiply the results

Exponentiation degree
For any number and a random natural numbers m and n
With the construction of the degree of the power base is left unchanged , and the figures are multiplied

Exponentiation fraction
For any numbers a and b >0 and any positive integer n
With the construction of the power fraction erected in the degree of the numerator and denominator of the fraction

History of the number of degree
In his famous book " Arithmetic " Diophantus of Alexandria described the first natural degree

Rene Descartes in his
"geometry" ( 1637 ) ,
we find the current
designation of degrees
а2,а3,...

" Silences " Game
1. Follow these steps:
х11∙х∙х2 ; х14 : х5 ; (а4)3 ; (-За)2.
2. Compare the expression to zero :
( - 5)7; (-6)18; (- 4)11. (-4)8 (- 5)18∙ (- 5)6; -(- 4)8.
3. Calculate the value of the expression :
-1∙ 32; (-1 ∙ 3)2 1∙(-3)2; - (2 ∙ 3)2; 12 ∙ (-3)2

THE GAME " THE PAIR OF NUMBERS "
Answers

ANSWERS :
(1, 4)
(2, 7)
(3, 6)
(4, 3)
(5, 2 )

Computational pause

Comparing expressions
Compare without performing calculations. Find the correct inequalities. From their respective letters make up the name of the architect , the project is the building of the Bolshoi Theater in Moscow was built in 1825 :

What number illustrates a circle?
Find out how many shows a circle, if the shaded portion shows a specified number . A record in the form of a
degree .

Reflection