Simplify:
$\frac{2 imes 3^4 imes 2^5}{9 imes 4}$

Q: Simplify: $\frac{2\times 3^4 \times 2^5}{9 \times 4}$

To simplify the expression $\frac{2 \times 3^4 \times 2^5}{9 \times 4}$, we need to follow the order of operations and simplify step by step. 1. **Calculate the powers:** - $3^4 = 81$ - $2^5 = 32$ 2. **Substitute these values back into the expression:** \[ \frac{2 \times 81 \times 32}{9 \times 4} \] 3. **Simplify the numerator:** - First, calculate $2 \times 32 = 64$. - Then, calculate $64 \times 81$. To simplify $64 \times 81$, we can break it down: \[ 64 \times 81 = 64 \times (80 + 1) = 64 \times 80 + 64 \times 1 \] \[ 64 \times 80 = 5120 \] \[ 64 \times 1 = 64 \] \[ 64 \times 81 = 5120 + 64 = 5184 \] 4. **Simplify the denominator:** - $9 \times 4 = 36$ 5. **Divide the simplified numerator by the simplified denominator:** \[ \frac{5184}{36} \] To perform this division, we can simplify: \[ 5184 \div 36 = 144 \] Thus, the simplified value of the expression is 144, which corresponds to Option 4. **Explanation for why other options are incorrect:** - **Option 1 (108):** This result does not match the calculated value of 144. The division of 5184 by 36 does not yield 108. - **Option 2 (72):** Similarly, dividing 5184 by 36 does not result in 72. This option is incorrect based on the calculation. - **Option 3 (18):** This is far from the calculated result of 144. The division of 5184 by 36 clearly does not equal 18. Therefore, based on the detailed calculation and simplification, Option 4 (144) is indeed the correct answer.

Question

Simplify: 
$\frac{2	imes 3^4 	imes 2^5}{9 	imes 4}$

Accepted Answer

To simplify the expression $\frac{2 \times 3^4 \times 2^5}{9 \times 4}$, we need to follow the order of operations and simplify step by step.

1. **Calculate the powers:**
   - $3^4 = 81$
   - $2^5 = 32$

2. **Substitute these values back into the expression:**
   $$
   \frac{2 \times 81 \times 32}{9 \times 4}
   $$

3. **Simplify the numerator:**
   - First, calculate $2 \times 32 = 64$.
   - Then, calculate $64 \times 81$.

To simplify $64 \times 81$, we can break it down:
   $$
   64 \times 81 = 64 \times (80 + 1) = 64 \times 80 + 64 \times 1
   $$
   $$
   64 \times 80 = 5120
   $$
   $$
   64 \times 1 = 64
   $$
   $$
   64 \times 81 = 5120 + 64 = 5184
   $$

4. **Simplify the denominator:**
   - $9 \times 4 = 36$

5. **Divide the simplified numerator by the simplified denominator:**
   $$
   \frac{5184}{36}
   $$

To perform this division, we can simplify:
   $$
   5184 \div 36 = 144
   $$

Thus, the simplified value of the expression is 144, which corresponds to Option 4.

**Explanation for why other options are incorrect:**

- **Option 1 (108):** This result does not match the calculated value of 144. The division of 5184 by 36 does not yield 108.
  
- **Option 2 (72):** Similarly, dividing 5184 by 36 does not result in 72. This option is incorrect based on the calculation.

- **Option 3 (18):** This is far from the calculated result of 144. The division of 5184 by 36 clearly does not equal 18.

Therefore, based on the detailed calculation and simplification, Option 4 (144) is indeed the correct answer.