简化 ((x4) (-3)) × 2x4

化简 ((x ⁴ ) (-3)) × 2x ⁴

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，

• 乘积规则 ⇢ 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

化简 ((x ⁴ )(-3)) × 2x ⁴ 。

解决方案：

As it is clearly seen, the entire problem statement is asking for a simplification using exponent rules, looking at the expression ((x⁴) (-3)) × 2x⁴. it is observed that only a few steps are required to solve the equation. Let’s look at the steps,

Step 1: Rearrange the terms to place coefficients on the left.

= (-3 x⁴) × (2 x⁴)

Step 2: Eliminate parenthesis not required.

= -3x⁴ × 2x⁴

Step 3: Multiply the coefficients and bring the variables together.

= -6 x⁴ × x⁴

Step 4: Use rules of exponents to combine them, (Here, use product rule).

= -6 x^{(4 + 4)}

= -6 x⁸

Therefore, the simplified form is -6 x⁸.

类似问题

问题 1：化简 ((y ⁶ ) (-2)) × -8y ⁴ 。

解决方案：

As it is clearly seen, the entire problem statement is asking for a simplification using exponent rules, looking at the expression ((y⁶) (-2)) × -8y⁴. it is observed that only a few steps are required to solve the equation. Let’s look at the steps,

Step 1: Rearrange the terms to place coefficients on the left.

= (-2 y⁶) × (-8 y⁴)

Step 2: Eliminate parenthesis not required.

= -2y⁶ × -8y⁴

Step 3: Multiply the coefficients and bring the variables together.

= 16 y⁶ × y⁴

Step 4: Use rules of exponents to combine them, (Here, use product rule).

= 16 y^{(6 + 4)}

= 16 y¹⁰

Therefore, the simplified form is 16 y¹⁰.

问题 2：简化 10(e ^x ) ²

解决方案：

As it is clearly seen, the entire problem statement is asking for a simplification using exponent rules, looking at the expression 10(e^x)², it is observed that x is the exponent of e and 2 is the exponent of ex, and 5 is constant, using the power rule of exponents, it can be written as,

Power Rule ⇢ (aⁿ)^m = a^{n × m}

10(e^x)² = 10(e^{x × 2})

= 10(e^2x)

问题 3：化简 [((y ⁷ ) (5))] ÷ [-5y ⁷ ]。

解决方案：

As it is clearly seen, the entire problem statement is asking for a simplification using exponent rules, looking at the expression [((y⁷) (5))] ÷ [-5y⁷]. it is observed that only a few steps are required to solve the equation. Let’s look at the steps,

Step 1: Rearrange the terms to place coefficients on the left.

= (5 y⁷) ÷ (-5 y⁷)

Step 2: Eliminate parenthesis not required.

= 5y⁷ ÷ -5y⁷

Step 3: Multiply the coefficients and bring the variables together.

= -25 y⁷ ÷ y⁷

Step 4: Use rules of exponents to combine them, (Here, use product rule).

= -25 y^{(7 – 7)}

= -25 y⁰

= -25

Therefore, the simplified form is -25.