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Telangana TET Paper 1 Exam Model Paper 2

Section: Mathematics

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Question : 118 of 150

Marks: +1, -0

Simplify:

((6^{4})^{2}\times \frac{1}{216^{2}})\times 6+16=?

224
242
216
232

Solution:

Concept:

Use laws of exponents and prime factorization to simplify powers of 6.

Explanation:

1. Write

(6^{4})^{2} = 6^{8}

.

2. Express

216 = 6^{3}

, so

216^{2} = 6^{6}

.

3. The expression becomes:

(6^{8} \times \frac{1}{6^{6}}) \times 6 + 16

4. Simplify the fraction:

6^{8} \times \frac{1}{6^{6}} = 6^{2}

.

5. Multiply:

6^{2} \times 6 = 6^{3} = 216

.

6. Finally add 16:

216 + 16 = 232

.

Answer:

232 (Option D)

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