# Exponents and Variable Equalities

• MHB
• RidiculousName
In summary: N has to be multiplied by both 2s before the exponent is applied. In summary, the exponent is applied before the multiplication in expressions like 2XN, which is why 2N+1 does not equal (2 * 2)N = 4N. N must be multiplied by both 2s before the exponent is applied to get 2^{N+1} = 2 \cdot 2^N \neq 4^N.
RidiculousName
I am not sure how to figure this out. Basically, I know XN + XN = 2XN and that 2N + 2N = 2N+1. So, since 2 * 2 = 4 why doesn't 2N+1 = (2 * 2)N = 4N?

Why did you put the brackets there? Then you have to distribute N over both twos, which is not what you started out with.

greg1313 said:
Why did you put the brackets there? Then you have to distribute N over both twos, which is not what you started out with.

Sorry, I am terrible with the syntax of math. How would I indicate that the 2s should be multiplied before the exponent is applied? (2(2))N?

(2 * 2)$^\text{N}$

Is this part of a problem you're working on? If so, please post it and I'll be better equipped to help. :)

RidiculousName said:
2N+1 = (2 * 2)N = 4N?
$$\displaystyle 2^{N + 1} = 2 \cdot 2^N \neq 4^N$$

-Dan

greg1313 said:
(2 * 2)$^\text{N}$

Is this part of a problem you're working on? If so, please post it and I'll be better equipped to help. :)

I'm not really working on a problem. I'm just trying to figure out why it doesn't fit. I want to know the concepts behind the numbers here.

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topsquark said:
$$\displaystyle 2^{N + 1} = 2 \cdot 2^N \neq 4^N$$

-Dan

Thank you. I think I've got it. Basically in 2XN the exponent is applied first. So that's why 2N + 2N = 2N+1 but not 4N

## What is an exponent?

An exponent is a number that represents the power or repeated multiplication of a base number. It is written as a superscript to the right of the base number.

## What is the difference between a base number and an exponent?

A base number is the number that is being multiplied by itself a certain number of times, while an exponent is the number that represents how many times the base number is being multiplied by itself.

## What is the rule for multiplying exponents?

When multiplying exponents with the same base, you add the exponents together. For example, 24 * 23 = 27.

## How do you solve equations with exponents?

To solve equations with exponents, you can use the properties of exponents to simplify the equation. If the bases are the same, you can equate the exponents and solve for the variable. If the bases are not the same, you can use logarithms to solve for the variable.

## What is a variable equality?

A variable equality is an equation that shows that two expressions are equal by using variables. It is a mathematical statement that shows that the values of two expressions are equivalent.

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