x⁻ⁿ
The expression x⁻ⁿ represents the reciprocal of x raised to the power of n
The expression x⁻ⁿ represents the reciprocal of x raised to the power of n. In other words, it is equivalent to 1 divided by xⁿ.
To understand this further, let’s break it down step by step:
Step 1: Start with xⁿ
The expression xⁿ means multiplying x by itself n times. For example, x³ means x * x * x.
Step 2: Take the reciprocal
To find the reciprocal, we divide 1 by xⁿ. This is denoted by x⁻ⁿ. For instance, if x = 2 and n = 4, then x⁻ⁿ = 1 / (2⁴) = 1 / (2 * 2 * 2 * 2) = 1/16.
It’s important to note that the negative exponent, indicated by the ⁻ⁿ, represents the inverse or reciprocal of the number raised to the positive exponent.
Here are a few additional properties of negative exponents that can be helpful:
1. Any non-zero number raised to the power of 0 is 1. So, x⁰ = 1 for any non-zero value of x.
2. When combining multiple exponents, the negative exponents can be rewritten as positive exponents by taking their reciprocal. For example, (x⁻³)⁻² can be simplified as (1/x³)⁻², which is equal to (x³)² = x⁶.
Negative exponents are frequently encountered in algebraic expressions, scientific notation, and various areas of mathematics and science. Understanding their meaning and properties helps in simplifying equations, solving problems, and performing calculations.
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