To simplify the expression \( (2^3 \times 2^2) \div 2^4 \) using the laws of indices, let's break it down step by step. ### Step 1: Apply the Law of Indices for Multiplication The first part of the expression is \( 2^3 \times 2^2 \). According to the laws of indices, when you multiply two powers with the same base, you add the exponents. This can be expressed as: \[ a^m \times a^n = a^{m+n} \] In our case: \[ 2^3 \times 2^2 = 2^{3+2} = 2^5 \] ### Step 2: Rewrite the Expression Now, we can rewrite the original expression using the result from Step 1: \[ (2^3 \times 2^2) \div 2^4 = 2^5 \div 2^4 \] ### Step 3: Apply the Law of Indices for Division Next, we need to simplify \( 2^5 \div 2^4 \). According to the laws of indices, when you divide two powers with the same base, you subtract the exponents. This can be expressed as: \[ \frac{a^m}{a^n} = a^{m-n} \] Applying this to our expression: \[ 2^5 \div 2^4 = 2^{5-4} = 2^1 \] ### Final Result Thus, the simplified result of the expression \( (2^3 \times 2^2) \div 2^4 \) is: \[ 2^1 \] ### Conclusion The correct option is **A. \( 2^1 \)**. ### Explanation of Other Options - **B. \( 2^0 \)**: This option is incorrect because \( 2^0 \) equals 1, which is not the result we obtained. The exponent zero indicates that the base is raised to zero, resulting in 1, which does not apply here. - **C. \( 2^{-1} \)**: This option is also incorrect. \( 2^{-1} \) equals \( \frac{1}{2} \), which is not the result of our simplification. Negative exponents indicate the reciprocal of the base raised to the positive exponent, which does not apply in this case. - **D. \( 2^2 \)**: This option is incorrect as well. \( 2^2 \) equals 4, which is not the result we calculated. This would imply that we added instead of subtracted the exponents in the division step. ### Revision Summary - Use the law of indices for multiplication: \( a^m \times a^n = a^{m+n} \). - Use the law of indices for division: \( \frac{a^m}{a^n} = a^{m-n} \). - Simplify step-by-step, ensuring to apply the correct operations for multiplication and division of powers. - The final answer for \( (2^3 \times 2^2) \div 2^4 \) is \( 2^1 \).