QQuestionMathematics
QuestionMathematics
Simplify (4x)−4. Write your answer using only positive exponents. Evaluate any numerical powers.
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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}}
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