b) $$ \left(2^{3} imes 2^{2} ight) \div 2^{7} $$

Question

b) $$ \left(2^{3} 	imes 2^{2}ight) \div 2^{7} $$

UpStudy AI · Accepted Answer

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
$$
\left(2^{3} \times 2^{2}\right) \div 2^{7} = \frac{1}{4}
$$
$$ \left(2^{3} \times 2^{2}\right) \div 2^{7} = \frac{1}{4} $$

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

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