Question:
Simplify the expression: $9^{18} \div 3^{14} \text{ of } 27^3 \times \sqrt{6561}$
व्यंजक को सरल कीजिए: $9^{18} \div 3^{14} \text{ of } 27^3 \times \sqrt{6561}$
Options:
- a) 3^16
- b) 3^15
- c) 3^18
- d) 3^17
- a) 3^16
- b) 3^15
- c) 3^18
- d) 3^17
correct answer : d)
Explanation:
Express all terms with base 3:
1. $9^{18} = (3^2)^{18} = 3^{36}$
2. $3^{14} \text{ of } 27^3 = 3^{14} \times (3^3)^3 = 3^{14} \times 3^9 = 3^{23}$ (using ‘of’ precedence, this is computed first)
3. $\sqrt{6561} = \sqrt{3^8} = 3^4 = 81$
Now substitute back:
$3^{36} \div 3^{23} \times 3^4 = 3^{36 – 23 + 4} = 3^{17}$.
Hence, option (d) is the correct answer.
सभी पदों को आधार 3 के रूप में व्यक्त करें:
1. $9^{18} = (3^2)^{18} = 3^{36}$
2. $3^{14} \text{ of } 27^3 = 3^{14} \times (3^3)^3 = 3^{14} \times 3^9 = 3^{23}$ (‘of’ की प्राथमिकता का उपयोग करते हुए, इसकी गणना पहले की जाती है)
3. $\sqrt{6561} = \sqrt{3^8} = 3^4 = 81$
अब मान वापस रखें:
$3^{36} \div 3^{23} \times 3^4 = 3^{36 – 23 + 4} = 3^{17}$।
अतः, विकल्प (d) सही उत्तर है।