Math Problem Statement

Rewrite f(x) = 1 / x^11 as a function with a negative power.

Solution

The question asks to rewrite the function f(x)=1x11f(x) = \frac{1}{x^{11}} as a function with a negative power.

Solution:

Using the property of exponents: 1xn=xn\frac{1}{x^n} = x^{-n} where nn is a positive integer.

So, we can rewrite f(x)=1x11f(x) = \frac{1}{x^{11}} as: f(x)=x11f(x) = x^{-11}

Thus, the answer is f(x)=x11f(x) = x^{-11}.

Would you like more details or have any other questions?

Here are some related questions to explore:

  1. How do negative exponents affect the function graph?
  2. What is the derivative of f(x)=x11f(x) = x^{-11}?
  3. How do you simplify expressions with negative exponents?
  4. Can you rewrite f(x)=1x11f(x) = \frac{1}{x^{11}} with a fractional exponent?
  5. How do negative exponents impact the domain of the function?

Tip: Remember, negative exponents represent reciprocals, making expressions easier to manipulate algebraically.

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents
Reciprocals

Formulas

1 / x^n = x^(-n)

Theorems

Properties of Exponents

Suitable Grade Level

Grades 8-10