xⁿ 同底数幂相乘Multiplying Exponents Calculator

使用说明与常见问题How-to & FAQ

「同底数幂相乘」是什么？What is the Multiplying Exponents Calculator tool?

同底数幂相乘指数相加：aᵐ × aⁿ = aᵐ⁺ⁿ；幂的乘方指数相乘：(aᵐ)ⁿ = aᵐⁿ；同指数不同底：aⁿ × bⁿ = (ab)ⁿ。给出化简式和数值。本地处理。Same base: add exponents, aᵐ × aⁿ = aᵐ⁺ⁿ; power of a power: (aᵐ)ⁿ = aᵐⁿ; same exponent: aⁿ × bⁿ = (ab)ⁿ. Shows the simplified form and the value. Processed locally.

如何使用「同底数幂相乘」？How do I use the Multiplying Exponents Calculator tool?

在「同底数幂相乘」中，填写「规则」、「底数 a」、「指数 m（或 n）」、「指数 n」、「底数 b（同指数时）」等参数，结果会随输入实时计算并显示在下方。In the Multiplying Exponents Calculator: Fill in "Rule", "Base a", "Exponent m (or n)", "Exponent n", "Base b (same exponent)"; results are recalculated instantly as you type.

不同底不同指数？Different bases and exponents?

aᵐ × bⁿ 一般不能合并，只能分别计算后相乘。aᵐ × bⁿ generally cannot be combined - compute each and multiply.

能举个计算实例吗？Can you show a worked example?

例如在「同底数幂相乘」中填 规则 = 同底 aᵐ × aⁿ，底数 a = 2，指数 m（或 n） = 3，指数 n = 4，底数 b（同指数时） = 5，结果区显示：化简：2^3 × 2^4 = 2^7；数值：128For example, entering Rule = Same base, Base a = 2, Exponent m (or n) = 3, Exponent n = 4, Base b (same exponent) = 5 in the Multiplying Exponents Calculator gives: Simplified: 2^3 × 2^4 = 2^7; Value: 128

哪些输入会被检查？Which inputs are validated?

「同底数幂相乘」会检查这些输入——「底数 a」、「指数 m（或 n）」：必须填写；「指数 n」、「底数 b（同指数时）」：所选方式用到时必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Multiplying Exponents Calculator checks its inputs — "Base a", "Exponent m (or n)": required; "Exponent n", "Base b (same exponent)": required when the chosen option uses it; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「同底数幂相乘」的设置：「规则」可选 同底 aᵐ × aⁿ、乘方 (aᵐ)ⁿ、同指数 aⁿ × bⁿ（默认 同底 aᵐ × aⁿ）；「底数 a」默认 2；「指数 m（或 n）」默认 3；「指数 n」默认 4；「底数 b（同指数时）」默认 5。每次生成结果都按当前设置处理。Settings in the Multiplying Exponents Calculator — "Rule": Same base, Power of a power, Same exponent (default Same base); "Base a" default 2; "Exponent m (or n)" default 3; "Exponent n" default 4; "Base b (same exponent)" default 5. The result always uses the current settings.

计算精度如何？How precise are the results?

「同底数幂相乘」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Multiplying Exponents Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「同底数幂相乘」免费吗？需要注册吗？Is the Multiplying Exponents Calculator free? Do I need an account?

「同底数幂相乘」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Multiplying Exponents Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.