Problem 12
Question
Evaluate each exponential expression. $$ 2^{-6} $$
Step-by-Step Solution
Verified Answer
\(\frac{1}{64}\)
1Step 1: Understanding Negative Exponents
An expression with a base 'b' and negative exponent '-n' is equal to 1 divided by the base 'b' to the power of the positive exponent 'n'. That is \(b^{-n} = \frac{1}{b^n}\). Apply this concept to the given exercise.
2Step 2: Apply the Principle
Substitute 'b' with 2 and 'n' with 6 in the formula. This means that \(2^{-6} = \frac{1}{2^6}\).
3Step 3: Evaluate the Expression
Now evaluate the expression formed. This requires calculating to what 2 raised to the power 6 equals. After the calculation, divide 1 by this value.
4Step 4: Final Calculation
2 raised to the power 6 is 64. So, \(2^{-6} = \frac{1}{2^6} = \frac{1}{64}\).
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Problem 12
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