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QuestionMathematics

Simplify (4x)−4. Write your answer using only positive exponents. Evaluate any numerical powers. The solution is ?
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Answer

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Step 1:
I'll solve this step by step, following the LaTeX formatting guidelines precisely:

Step 2:
: Understand the expression

The problem asks us to simplify $$\left(4x\right)^{-4}$$ and rewrite it with positive exponents.

Step 3:
: Rewrite using the power rule of exponents

\left(4x\right)^{-4} = \frac{1}{\left(4x\right)^{4}}
When we have a power raised to a negative exponent, we can rewrite it as a reciprocal with a positive exponent:

Step 4:
: Expand the denominator

\frac{1}{\left(4x\right)^{4}} = \frac{1}{4^{4} \cdot x^{4}}

Step 5:
: Calculate the numerical power

4^{4} = 256

Step 6:
: Simplify the final expression

\frac{1}{256 \cdot x^{4}} = \frac{1}{256x^{4}}

Final Answer

\frac{1}{256x^{4}}