如何将数字表示为 2 的幂？

数学不仅与数字有关，而且与涉及数字和变量的不同计算有关。这就是基本上被称为代数的东西。代数被定义为涉及由数字、运算符和变量组成的数学表达式的计算的表示。数字可以是 0 到 9，运算符是数学运算符，如 +、-、×、÷、指数等，变量如 x、y、z 等。

指数和幂

指数和幂是数学计算中使用的基本运算符，指数用于简化涉及多次自乘的复杂计算，自乘基本上是数字与自身相乘。例如，7 × 7 × 7 × 7 × 7，可以简单地写成 7 ⁵ 。这里，7 是基值，5 是指数，值为 16807。11 × 11 × 11，可写为 11 ³ ，这里，11 是基值，3 是 11 的指数或幂。 11 ³是 1331。

指数被定义为一个数字的幂，它乘以自身的次数。如果表达式写成 cx ^y其中 c 是常数，c 将是系数，x 是底数，y 是指数。如果一个数 p 乘以 n 次，n 将是 p 的指数。它将被写为

p × p × p × p … n 次 = p ⁿ

指数的基本规则

为了求解指数表达式以及其他数学运算，为指数定义了一些基本规则，例如，如果有两个指数的乘积，则可以简化以使计算更容易，称为乘积规则，让我们看一下指数的一些基本规则，

• 乘积法则 ⇢ a ⁿ + a ^m = a ^{n + m}
• 商规则 ⇢ a ⁿ / a ^m = a ^{n – m}
• 幂律 ⇢ (a ⁿ ) ^m = a ^{n × m}或^m √a ⁿ = a ^n/m
• 负指数规则 ⇢ a ^-m = 1/a ^m
• 零规则 ⇢ a ⁰ = 1
• 一条规则 ⇢ a ¹ = a

如何将数字表示为 2 的幂？

解决方案：

Any number having a power of 2 can be written as the square of that number. The square of a number of a number is the number multiplied by itself, square of the number is represented as the exponent 2 on that number. If square of x has to be written, it will be x². For instance, the square of 3 is represented as 5² and is equal to 5 × 5 = 25. Another example can be the square of 12, represented as 12², is equal to 12 × 12 = 144. Lets take the number 3, now 3 as the power of 2 will be represented as,

3² = 3 × 3

= 9

Therefore, 9 is the 2nd power of 3.

Hence, it can be concluded that any number as a power of 2 can be represented as the square of that number. 

示例问题

问题 1：求解表达式 5 ² – 3 ² 。

解决方案：

To solve the expression, first solve the 2^nd powers on the numbers and then subtract the second term by the first term. However, the same problem can be solved in an easier way by simply applying a formula, the formula is,

x² – y² = (x + y)(x – y)

5² – 3² = (5 + 3)(5 – 3)

= 8 × 2

= 16

问题 2：求解表达式 10 ² – 6 ² 。

解决方案：

To solve the expression, first solve the 2^nd powers on the numbers and then subtract the second term by the first term. However, the same problem can be solved in an easier way by simply applying a formula, the formula is,

x² – y² = (x + y)(x – y)

10² – 6² = (10 + 6)(10 – 6)

= 16 × 4

= 64

问题 3：求解表达式 8 ² + 2 ² 。

解决方案：

To solve the expression, first solve the 2^nd powers on the numbers and then add the second term by the first term.

8² + 2² = (8 × 8) + (2 × 2)

= 64 + 4

= 68