To simplify the expression \( (2^3 \times 2^{-5}) \) and express the answer in standard form, let's go through the steps carefully. ### Step 1: Apply the Laws of Exponents When multiplying numbers with the same base, we can use the law of exponents that states: \[ a^m \times a^n = a^{m+n} \] In our case, the base is \( 2 \), and we have: - \( m = 3 \) - \( n = -5 \) So, we can combine the exponents: \[ 2^3 \times 2^{-5} = 2^{3 + (-5)} = 2^{3 - 5} = 2^{-2} \] ### Step 2: Express in Standard Form The expression \( 2^{-2} \) can be rewritten in standard form. The negative exponent indicates that we take the reciprocal: \[ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \] ### Final Answer Thus, the simplified expression \( (2^3 \times 2^{-5}) \) in standard form is: \[ \frac{1}{4} \] ### Correct Option The correct option is **B. \( \frac{1}{4} \)**. ### Explanation of Other Options - **Option A: \( \frac{1}{8} \)**: This is incorrect because \( 2^{-2} \) simplifies to \( \frac{1}{4} \), not \( \frac{1}{8} \). \( \frac{1}{8} \) corresponds to \( 2^{-3} \). - **Option C: \( 2^{-2} \)**: While this is a correct intermediate step in the simplification process, it is not in standard form. The question specifically asks for the expression in standard form, which is \( \frac{1}{4} \). - **Option D: \( 2^{-1} \)**: This is incorrect because \( 2^{-1} \) equals \( \frac{1}{2} \), which does not match our simplified expression. ### Summary of Key Points - Use the law of exponents to combine terms with the same base. - A negative exponent indicates the reciprocal of the base raised to the positive exponent. - The final answer should be expressed in standard form, which is typically a fraction or a decimal. - The correct answer for the expression \( (2^3 \times 2^{-5}) \) is \( \frac{1}{4} \).