Question

evaluate the expression (2^{-3} cdot 2^{4}). simplify. 2^{-3} cdot 2^{4} = 2^{1} =? with options (\frac{1}{2}), (1), (1\frac{1}{2}), (2)

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we use the rule \(a^m \cdot a^n = a^{m + n}\). First, we already combined the exponents: \(2^{-3}\cdot2^{4}=2^{-3 + 4}=2^{1}\).

Step2: Evaluate \(2^{1}\)

Any number to the power of 1 is the number itself, so \(2^{1}=2\).

Answer:

2