简化 (x ² )(x ⁵ )

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

简化 (x ² )(x ⁵ )

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 (x²)(x⁵), it is observed that product rule of exponents can be easily applied on this expression,

Product Rule ⇢ aⁿ × a^m = a^{n + m}

x² × x⁵ = x^{(2 + 5)}

= x⁷

Therefore, x⁷ is the value obtained.

类似问题

问题 1：化简 3(y ⁵ ) ²

解决方案：

It is observed that 5 is the exponent of y and 2 is the exponent of y⁵, and 3 is constant, using the power rule of exponents, it can be written as,

Power Rule ⇢ (aⁿ)^m = a^{n × m}

3(y⁵)² = 3y^{(5 × 2)}

= 3y¹⁰

问题 2：化简 (x ¹⁷ )(x ²³ )

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 (x¹⁷)(x²³), it is observed that product rule of exponents can be easily applied on this expression,

Product Rule ⇢ aⁿ × a^m = a^{n + m}

x¹⁷ × x²³ = x^{(17 + 23)}

= x⁴⁰

Therefore, x⁴⁰ is the value obtained.

问题 2：简化 47(x ¹⁰ )(x ⁸⁹ )

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 47(x¹⁰)(x⁸⁹), it is observed that product rule of exponents can be easily applied on this expression,

Product Rule ⇢ aⁿ × a^m = a^{n + m}

47[x¹⁰ × x⁸⁹] = 47x^{(10 + 89)}

= 47x⁹⁹

Therefore, 47x⁹⁹ is the value obtained.