Evaluate 10^(-4).
Understand the Problem
The question is asking to evaluate the expression 10^(-4), which involves understanding negative exponents and how to rewrite them as fractions.
Answer
The value of \( 10^{-4} \) is \( \frac{1}{10000} \).
Answer for screen readers
The value of ( 10^{-4} ) is ( \frac{1}{10000} ).
Steps to Solve
- Understanding Negative Exponents
Negative exponents indicate that you should take the reciprocal of the base raised to the opposite positive exponent.
- Rewrite the Expression
For $10^{-4}$, this can be rewritten using the property of negative exponents:
$$ 10^{-4} = \frac{1}{10^{4}} $$
- Calculate $10^{4}$
Next, calculate $10^4$:
$$ 10^4 = 10 \times 10 \times 10 \times 10 = 10000 $$
- Substitute and Simplify
Substitute the result back into the expression:
$$ 10^{-4} = \frac{1}{10000} $$
The value of ( 10^{-4} ) is ( \frac{1}{10000} ).
More Information
This expression shows how negative exponents can indicate very small values, as they are used frequently in scientific notation to represent numbers less than one.
Tips
- Forgetting to use the reciprocal when dealing with negative exponents.
- Not calculating the positive exponent correctly, leading to an incorrect final answer.
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