3的4次方是多少？

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，可以写为 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。它会写成，

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

3 的 4^次方是多少？

解决方案：

Any number having a power of 4 can be written as the quartic of that number. The quartic of a number is the number multiplied by itself four times, quartic of the number is represented as the exponent 4 on that number. If quartic of x has to be written, it will be x⁴. For instance, the quartic of 5 is represented as 5⁴ and is equal to 5 × 5 × 5 × 5 = 625. Another example can be the quartic of 12, represented as 12⁴, is equal to 12 × 12 × 12 × 12 = 20736.

Let’s come back to the problem statement and understand how it will be solved, the problem statement asked to simplify 3 to the 4^th power. It means the question asks to solve the quartic of 3, which is represented as 3⁴,

3⁴ = 3 × 3 × 3 × 3

= 9 × 3 × 3

= 81

Therefore, 81 is the 4^th power of 3.

示例问题

问题 1：求解表达式 6 ³ – 2 ³ 。

解决方案：

To solve the expression, first solve the 3^rd 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,

x³ – y³ = (x – y)(x² + y² + xy)

6³ – 2³ = (6 – 2)(6² + 2² + 6 × 2)

= 4 × (36 + 4 + 12)

= 4 × 52

= 208

问题 2：求解表达式 7 ² – 5 ² 。

解决方案：

To solve the expression, first solve the 2nd 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)

7² – 5² = (7 + 5)(7 – 5)

= 12 × 2

= 24

问题 3：求解表达式 3 ³ + 3 ³ 。

解决方案：

To solve the expression, first solve the 3^rd 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,

x³ + y³ = (x + y)(x² + y² – xy)

3³ + 3³ = (3 + 3)(3² + 3² – 3 × 3)

= 6 × (9 + 9 – 9)

= 6 × 9

= 54

Another method of solving it is to simply calculate the cube of each term and then add both the terms,

3³ + 3³ = 27 + 27

= 54