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The concept of power

The meaning of 1. power, the names of each part and the reading and writing in A n, the same multiplier A is called the base, the number N of A is called the exponent, and the result of power operation A n is called the power (pronounced mi). A n is pronounced as the n power of A. If A n is regarded as the result of power, it is pronounced as the n power of A, and the quadratic power of A (or the quadratic power of A) can also be pronounced as the square of A; The cubic power of a (or the cubic power of a) can also be read as the cube of a. Every natural number can be regarded as the first power of this number, also called the first power. For example, 8 can be regarded as 8 1. When the index is 1, it is usually omitted. Operation order: power first, then parentheses, then multiplication and division, and addition and subtraction at the end. The product of 1. multiplied by the same multiplier is expressed as a power. 2. Calculate the answer1) 9 4 according to the meaning of power; 2)0^6。 9 4 = 9×9×9 = 656 1 We can see that 0 n = 0 (n is a positive number) p.s: n 0 = 1 (n ≠ 0) 4. Distinguish the concepts of 1) 8 3 and 8. 2) 5×2 and 5× 2; 3) 4× 5 2 and (4× 5) 2. 5. Calculate the decimal power of a number. If the decimal is a rational number, change it into the form of p/q (that is, fraction). Then the p/q power of any number n is equal to the p power of n and then open the root number q times.

Edit the multiplication and division rules of the same radix power in this paragraph.

Same base powers's law of multiplication: same base powers multiplies and divides, the original base is the base, and the sum or difference of indexes is the index. Expressed in letters: a m× an n = a (m+n) or a m ÷ an n = a (m-n) (both m and n are natural numbers) 1) 15 2× 15. 2)3^2×3^4×3^8; 3)5×5^2×5^3×5^4×…×5^90 1) 15^2× 15^3= 15^(2+3)= 15^5 2)3^2×3^4×3^8=3^(2+4+8)=3^ 14 3)5×5^2×5^3×5^4×…×5^90=5^( 1+2+3+…+90)=5^4095

Edit this paragraph of power law.

An m is also called power. If an m is taken as the base, its n power can be expressed as (a m) n, which is called the power of the power. Let's count (a 3) 4 first. Taking A 3 as the base, according to the meaning of power and same base powers's multiplication rule, we can get: (A 3) 4 = A 3× A 3× A 3 = A (3+3+3+3) = A (3× 4) = A 653. (A2) 5 = A2× A2× A2× A2 = A (2+2+2+2) = A (2× 5) = A10, that is: (A2: (A M) N = A (M× N) (X 4) 2; (a^2)^4×(a^3)^5(x^4)^2=x^(4×2)=x^8(a^2)^4×(a^3)^5=a^(2×4)×a^(3×5)=a^8×a^ 15=a^(8+ 15)=a^23

Edit the function of this product.

Multiply the product, first multiply each multiplier in the product separately, and then multiply the obtained power. Expressed in letters as: (a× b) n = a n× b n The power law of this product also applies to the power of the product of more than three multipliers. For example: (a× b× c) n = a n× b n× c n am times a power, (m, n is a positive integer) Independent inquiry: after the formula is reversed, it can also be called "exponential power multiplication", that is, it is multiplied by exponential power, the index is unchanged, and the base is multiplied. a^n*b^n=(ab)^n

Edit the square difference formula of this paragraph (junior high school textbook)

The sum of two numbers multiplied by the difference of two numbers is equal to the square of the difference of two numbers. Expressed in letters: (a+b) × (a-b) = a 2-b 2 This formula is called the square difference formula. Using this formula, some calculations can be simplified. Use a simple method to calculate 104×96. Solution: Original formula = (100+4) × (100-4) =1002-42 =10000-16 = 9984 cases: known a =2.

Edit the complete square formula in this paragraph (junior high school textbook)

The square of the sum (or difference) of two numbers is equal to the sum of their squares plus (or minus) times their product. Expressed in letters: (a+b) 2 = a 2+2ab+b 2 or (a-b) 2 = a 2-2ab+b 2. The above two formulas are called complete square formulas. The application of complete square formula can make the calculation of some powers simple. Calculate the following questions:1)1052; 2) 196^2。 1) 105^2=( 100+5)^2= 100^2+2× 100×5+5^2= 10000+ 1000+25= 1 1025 2) 196^2=(200-4) ^2=200^2-2×200×4+4^2=40000- 1600+ 16=384 16

Edit the quick calculation of the square of this paragraph.

The square of some special numbers can speed up the calculation after mastering the law, which is introduced as follows. 1. Find the square of the number composed of n 1 Let's observe the following example. 1^2= 1 1 1^2= 12 1 1 1 1^2= 1232 1 1 1 1 / kloc-0/^2= 12343265438+ 0 1 1 1 1 2 = 12345432 1 1 1 1 1 1 65438. Find the square of the number composed of n 1, write it from 1 to n, and then write it from n to 1, that is,12 =1234 ... (n-/kloc- 2. Let's observe the square of the number composed of n 3: 3 2 = 9 33 2 =1089 333 2 =110889 333 2 =/kloc-0. 5438+0088889 Therefore, it can be seen that: 33 … 3 2 =11088 … 889 n 3 (n-1)1(n-/kloc-. In a completely flat manner; ( 10a+5)2 =( 10a)2+2× 10a×5+5 2 = 100 a 2+ 100 a+25 = 100 a×。 It is the square of the number 5, which is equal to the number multiplied by the product of 1 after removing the single digits, and then write 25. Example calculation1) 45 2; 2) 1 15^2。 Solution: 1) Original formula = 4× (4+ 1 )× 100+252) Original formula =11× (11). = 2025 =13200+25 =13225 4. The multiplication with the same exponential power A 2× B 2 is the multiplication with the same exponential power, which can be written as: A 2× B 2 = A× A× B = (A× B )× (. According to this law, the calculation can be simplified. For example, 22× 52 = (2× 5) 2 =102 =10023 = (2× 5) 3 =10002.

Edit this exercise

1. Calculate the following problem according to the meaning of power:1) 8 32)103) 0 44) 2 508 3 = 8× 8 = 5121. 5438+0×1×1×1=104 = 0× 0× 0× 0 = 0250 = 2× 2×…× 2× 250. Why? 1) 5 2 and 5× 2; 2) 5 3 and 3 5; 3) 2× 3 4 and (2× 3) 4. No, 5 2 = 5× 5 is different, 5 3 = 5× 5× 5 and 3 5 = 3× 3× 3× 3. (2×3) 4 = 2 4× 3 4 3. Calculate the following problems: 43× 4432× 33485 ÷ 83364 ÷ 36 (92) 3 (A3) 5 = 8+06 2 = (100+3) (. 00× 8+8 2 =10 2+2×10× 6+6 2 =100 2-3 2 =10000+16000. =(2×5)^7= 10^7