Mastering Negative Exponents: Simplify Math Expressions Effortlessly

x^-n

y-y₁=m(x-x₁)

The expression x^-n represents the reciprocal of x^n, where n is a positive integer. In other words, x^-n can be written as 1/x^n. For example, if x = 2 and n = 3, then x^-n = 1/2^3 = 1/8.

It’s important to note that when n is an even number, x^n will always be positive since an even number times itself will always result in a positive value. Therefore, x^-n will also be positive. However, when n is an odd number, x^n can be positive or negative depending on the sign of x. Therefore, x^-n can also be positive or negative.

Another important thing to remember is that the value of x cannot be zero since any number raised to the power of negative infinity (which is what x^-n represents when n approaches infinity) is undefined.

To simplify expressions with negative exponents, we can use the following rules:

1. x^-n = 1/x^n
2. x^a * x^b = x^(a+b)
3. 1/x^-n = x^n

By applying these rules, we can rewrite expressions with negative exponents in a more simplified form.

More Answers: