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:

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

## Comments

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TopNewestThanks for reminding me. – Shraman Das · 2 years, 5 months ago

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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. – Arnab Laha · 2 years, 4 months ago

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– Arron Kau Staff · 2 years, 4 months ago

Arnab, you have to perform operations in parentheses first.Log in to reply

– Arnab Laha · 2 years, 3 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? :)Log in to reply

positiveroot, in this case). – Arron Kau Staff · 2 years, 3 months agoLog in to reply

thanks for the note.. – Shashwata Samanta · 2 years, 4 months ago

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