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:

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

Easy Math Editor

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`bold` or `__bold__`	bold
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1. numbered 2. list	numbered list
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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Thanks for reminding me.

Shraman Das - 6 years, 9 months ago

thanks for the note..

Shashwata Samanta - 6 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.

Arnab Laha - 6 years, 8 months ago

Arnab, you have to perform operations in parentheses first.

Arron Kau Staff - 6 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? :)

Arnab Laha - 6 years, 8 months ago

@Arnab Laha – 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).

Arron Kau Staff - 6 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$