Simplifying expression with exponents

In summary, when we have a negative symbol in front of an expression, it only applies to the first item. So for $(-4x)^n$, it would be equal to $(-4)^n \cdot x^n$ or $4^n \cdot (-x)^n$. However, $-4x^n$ is equal to $-4 \cdot x^n$, not $-4 \cdot (-x)^n$. To make the other items negative, we would have to distribute the negative symbol individually, as in $x(-b)(-c)w$.
  • #1
tmt1
234
0
Supposing I have

$$(-4x^n)$$

Why does it equal $(-4)^n * x^n$ and not $(-4)^n * (-x) ^ n$?

When we have a negative symbol it only applies to the first item in an expression? so $-xbcw$ equals $b * c * w * (-x)$? Which means if we wanted the other items to be negative we would have to do $x(-b)(-c)w$ (for $b$ and $c$ to be negative and the other items to be positive)?
 
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  • #2
Essentially you have $-4x^n$ which is equal to $-4\cdot x^n$.

If you intended $(-4x)^n$ then we have $(-4x)^n=(-4)^n\cdot x^n$ or $4^n\cdot (-x)^n$.

$-4\cdot-x=4x$ not $-4x$.

Does that help?
 
  • #3
greg1313 said:
Essentially you have $-4x^n$ which is equal to $-4\cdot x^n$.

If you intended $(-4x)^n$ then we have $(-4x)^n=(-4)^n\cdot x^n$ or $4^n\cdot (-x)^n$.

$-4\cdot-x=4x$ not $-4x$.

Does that help?

So, in no uncertain terms, $(-4)^n\cdot x^n$ equals $4^n\cdot (-x)^n$ ?
 
  • #4
Yes.
 

FAQ: Simplifying expression with exponents

What is an exponent?

An exponent is a number that represents how many times a base number is multiplied by itself. It is usually written as a small number above and to the right of the base number.

How do you simplify an expression with exponents?

To simplify an expression with exponents, you can use the rules of exponents, which include multiplying exponents with the same base, dividing exponents with the same base, and raising a power to a power.

Can you simplify an expression with negative exponents?

Yes, you can simplify an expression with negative exponents by using the rule that states a negative exponent is equal to the reciprocal of the base raised to the positive exponent.

What is the difference between a variable and an exponent?

A variable is a symbol that represents an unknown value, while an exponent is a number that represents how many times a base number is multiplied by itself. Variables can have different values, while exponents are constant.

Why is it important to simplify expressions with exponents?

Simplifying expressions with exponents allows for easier calculations and helps to understand the relationship between different variables in an expression. It also allows for a clearer representation of the underlying mathematical relationships.

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