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2.) $2^{-1} \\bullet 2^{-2} = $

Question

2.) $2^{-1} \bullet 2^{-2} = $

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$.
$2^{-1} \cdot 2^{-2} = 2^{-1 + (-2)}$

Step2: Calculate the sum of exponents

Simplify the exponent value.
$2^{-1 + (-2)} = 2^{-3}$

Step3: Convert negative exponent to fraction

Use the rule $a^{-k} = \frac{1}{a^k}$.
$2^{-3} = \frac{1}{2^3}$

Step4: Evaluate the positive exponent

Calculate the value of the denominator.
$\frac{1}{2^3} = \frac{1}{8}$

Answer:

$\frac{1}{8}$