b) \( \left(2^{3} \times 2^{2}\right) \div 2^{7} \)

To simplify the expression \( \left(2^{3} \times 2^{2}\right) \div 2^{7} \), we can use the properties of exponents. Let's break it down step by step. ### Step 1: Multiply the Powers with the Same Base When multiplying two exponents with the same base, you add the exponents: \[ 2^{3} \times 2^{2} = 2^{3+2} = 2^{5} \] So the expression becomes: \[ \frac{2^{5}}{2^{7}} \] ### Step 2: Divide the Powers with the Same Base When dividing two exponents with the same base, you subtract the exponents: \[ \frac{2^{5}}{2^{7}} = 2^{5-7} = 2^{-2} \] ### Step 3: Simplify the Negative Exponent A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent: \[ 2^{-2} = \frac{1}{2^{2}} = \frac{1}{4} \] ### Final Answer \[ \left(2^{3} \times 2^{2}\right) \div 2^{7} = \frac{1}{4} \]