Question

evaluate the expression $2^{-3} \cdot 2^{4}$. simplify. $2^{-3} \cdot 2^{4} = $? options: $2^{-7}$, $2^{-1}$, $2^{1}$, $2^{7}$

Explanation:

Step1: Recall exponent rule

When multiplying exponents with the same base, we use the rule \( a^m \cdot a^n = a^{m + n} \). Here, \( a = 2 \), \( m = -3 \), and \( n = 4 \).

Step2: Apply the rule

So, \( 2^{-3} \cdot 2^{4}=2^{-3 + 4} \).

Step3: Simplify the exponent

Calculate \( -3 + 4 = 1 \), so we have \( 2^{1} \).

Answer:

\( 2^{1} \) (or just 2, but in the given options, it's \( 2^{1} \))