To solve the expression \( (2^3 \times 2^4) \div 2^5 \) and find its equivalent in standard form, we will break it down step-by-step. ### Step 1: Simplify the Multiplication First, we need to simplify the multiplication part of the expression, which is \( 2^3 \times 2^4 \). According to the laws of exponents, when you multiply two powers with the same base, you add the exponents: \[ a^m \times a^n = a^{m+n} \] Applying this rule here: \[ 2^3 \times 2^4 = 2^{3+4} = 2^7 \] ### Step 2: Simplify the Division Next, we take the result from the multiplication and divide it by \( 2^5 \): \[ (2^3 \times 2^4) \div 2^5 = 2^7 \div 2^5 \] Again, we use the laws of exponents for division, which state that when you divide two powers with the same base, you subtract the exponents: \[ a^m \div a^n = a^{m-n} \] Applying this rule: \[ 2^7 \div 2^5 = 2^{7-5} = 2^2 \] ### Final Answer Thus, the expression \( (2^3 \times 2^4) \div 2^5 \) simplifies to \( 2^2 \). ### Correct Option The correct option is **A. \( 2^2 \)**. ### Explanation of Other Options Now, let's analyze the other options to understand why they are incorrect: - **B. \( 2^0 \)**: This represents the number 1, as any non-zero number raised to the power of 0 equals 1. Since we found that the expression simplifies to \( 2^2 \), this option is incorrect. - **C. \( 2^1 \)**: This represents the number 2. Since our simplified expression is \( 2^2 \), which equals 4, this option is also incorrect. - **D. \( 2^3 \)**: This represents the number 8. Again, since our simplified expression is \( 2^2 \), this option is incorrect as well. ### Summary of Key Points - When multiplying powers with the same base, add the exponents: \( a^m \times a^n = a^{m+n} \). - When dividing powers with the same base, subtract the exponents: \( a^m \div a^n = a^{m-n} \). - The expression \( (2^3 \times 2^4) \div 2^5 \) simplifies to \( 2^2 \). - The correct answer is **A. \( 2^2 \)**, while the other options do not match the simplified expression. This thorough breakdown should help you understand how to manipulate expressions with exponents and why the correct answer is \( 2^2 \).