简化 2m2×(2m3)

化简 2m ² ×(2m ³ )

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

什么是 2m ² (2m ³ )？

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 2m²(2m³), it is observed that the product rule of exponents can be easily applied to this expression,

Step 1: Remove the parenthesis and write terms with their exponents.

2m²(2m³) = 2m² × 2m³

Step 2: Apply the Product rule of exponents.

Product Rule ⇢ aⁿ × a^m = a^{n + m}

2m² × 2m³ = 2m^{(2 + 3)}

Therefore, 2m⁵ is the value obtained.

类似问题

问题1：什么是9m ⁵ (8m 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 9m⁵(8m⁷), it is observed that the product rule of exponents can be easily applied to this expression,

Step 1: Remove the parenthesis and write terms with their exponents.

9m⁵(8m⁷) = 9m⁵ × 8m⁷

Step 2: Apply the product rule of exponents.

Product Rule ⇢ aⁿ × a^m = a^{n + m}

9m⁵ × 8m⁷ = 9 × 8m^{(5 + 7)}

Therefore, 72m¹² is the value obtained.

问题 2：化简 (x ⁷ )(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 (x⁷)(x²), it is observed that the product rule of exponents can be easily applied to this expression,

Product Rule ⇢ aⁿ × a^m = a^{n + m}

x⁷ × x² = x^{(7 + 2)}

= x⁹

Therefore, x40 is the value obtained.

问题 2：化简 50(x ⁰ )(x ⁹ )

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 50(x⁰)(x⁹), it is observed that the product rule of exponents can be easily applied to this expression,

Product Rule ⇢ aⁿ × a^m = a^{n + m}

50[x⁰ × x⁹] = 50x^{(0 + 9)}

= 50x⁹

Therefore, 50x⁹ is the value obtained.