Simplifying this absolute value

If ##n## is positive, then the absolute value can be ignored if ##r## is also positive. Otherwise, if ##r## is negative, the sign will be flipped and the absolute value will have to be taken into account.
  • #1
Mr Davis 97
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I have the expression ##|nr^n|^{1/n}##. A quick question is whether I can allow the exponent to go inside of the absolute value. I know that if it were an positive integral exponent then because of the multiplicativity of the absolute value function that would be allowed. But I'm not sure what I'm allowed to do in the case of this rational exponent...
 
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  • #2
In the real numbers that works.
 
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  • #3
Mr Davis 97 said:
whether I can allow the exponent to go inside of the absolute value.

Are you asking whether ##|n r^n|^{1/n} = | (n r^n)^{1/n}| ## ?

Try ##r = 1,\ n = -2##.
 
  • #4
Stephen Tashi said:
Are you asking whether ##|n r^n|^{1/n} = | (n r^n)^{1/n}| ## ?

Try ##r = 1,\ n = -2##.
So it's not generally true then? What if ##n## is positive?
 
  • #5
If n and r are both positive then absolute value can be ignored.
 
  • #6
mathman said:
If n and r are both positive then absolute value can be ignored.
Well ##n## is positive while ##r## is not necessarily positive.
 

What is an absolute value?

An absolute value is the distance of a number from zero on a number line. It is always positive, regardless of the sign of the number.

How do you simplify an absolute value expression?

To simplify an absolute value expression, you need to remove the absolute value brackets and rewrite the expression as two separate equations, one with a positive sign and one with a negative sign. Solve each equation separately and then combine the solutions.

What are the rules for simplifying absolute value expressions?

The rules for simplifying absolute value expressions include: 1) if the absolute value is of a positive number, remove the brackets and keep the number as is, 2) if the absolute value is of a negative number, remove the brackets and change the sign of the number, 3) if the absolute value is of a variable, remove the brackets and write two equations, one with a positive sign and one with a negative sign, and 4) if the absolute value is of an expression, apply the distributive property and then simplify.

Can you simplify an absolute value with variables?

Yes, you can simplify an absolute value with variables by following the rules mentioned above. However, the final solution may involve an absolute value, unless the variable can be eliminated by solving the equations.

Why is it important to simplify absolute value expressions?

Simplifying absolute value expressions helps to make them easier to work with and understand. It also allows us to solve equations and inequalities involving absolute value more accurately and efficiently.

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