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# Rules of Exponents

Here are some basic rules for operations with exponents:

\begin{align} x^m \times x^n &= x^{m+n} \\ \frac{x^m}{x^n} &= x^{m-n} \\ x^{-n} &= \frac{1}{x^n} \\ (x^m)^n &= x^{mn} \\ (xy)^{n} &= x^n y^n \\ \left(\frac{x}{y}\right)^m &= \frac{x^m}{y^m} \end{align}

Radicals are just numbers with fractional indices, e.g. $$\sqrt[3]{7^2} = 7^{2/3}$$. Any operation with exponents can be applied to radicals, and they are related through this rule:

$x^{m/n} = \sqrt[n]{x^m}$

Note by Arron Kau
2 years, 9 months ago

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Thanks for reminding me. · 2 years, 9 months ago

I have an issue with the answer to the solution for the problem in this site. ((-5)^10)^(3/10)=125. Why should it not be +-125? I need an explanation. · 2 years, 8 months ago

Arnab, you have to perform operations in parentheses first. Staff · 2 years, 8 months ago

Is that so easy? Not for me at-least. What is (9765625)^(1/10)? Will it be +5 or -5 or +-5. Lets think about it carefully? :) · 2 years, 7 months ago

In the absence of reasons otherwise or clear specification, convention is to assume that we're looking for the principle root (i.e., the positive root, in this case). Staff · 2 years, 7 months ago