To simplify the expression \( (2^3 \times 2^{-5}) \) and express it in standard form, let's break it down step-by-step. ### Step 1: Understanding Exponents When multiplying numbers with the same base, you can add their exponents. This is a fundamental property of exponents, which states: \[ a^m \times a^n = a^{m+n} \] In our case, the base is \( 2 \), and we have: \[ 2^3 \times 2^{-5} \] ### Step 2: Applying the Exponent Rule Now, we can apply the exponent rule: \[ 2^3 \times 2^{-5} = 2^{3 + (-5)} = 2^{3 - 5} = 2^{-2} \] ### Step 3: Converting to Standard Form Next, we need to express \( 2^{-2} \) in standard form. The negative exponent indicates that we should take the reciprocal of the base raised to the positive exponent: \[ 2^{-2} = \frac{1}{2^2} \] Calculating \( 2^2 \): \[ 2^2 = 4 \] Thus, we have: \[ 2^{-2} = \frac{1}{4} \] ### Step 4: Expressing in Decimal Form To express \( \frac{1}{4} \) in decimal form, we can perform the division: \[ \frac{1}{4} = 0.25 \] ### Conclusion: Final Answer The simplified expression \( (2^3 \times 2^{-5}) \) in standard form is \( 0.25 \). Therefore, the correct option is: **C. \( 0.25 \)** ### Explanation of Other Options - **A. \( 0.125 \)**: This value corresponds to \( \frac{1}{8} \), which is not the result of our simplification. - **B. \( 0.5 \)**: This value corresponds to \( \frac{1}{2} \), which is also not the result of our simplification. - **D. \( 1 \)**: This value corresponds to \( 2^0 \), which is not applicable here since we have a negative exponent. ### Revision Summary - When multiplying powers with the same base, add the exponents. - A negative exponent indicates the reciprocal of the base raised to the positive exponent. - \( 2^{-2} \) simplifies to \( \frac{1}{4} \), which is \( 0.25 \) in decimal form. - The correct answer is \( 0.25 \) (Option C).