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Telangana TET Paper 1 Exam Model Paper 2

Section: Mathematics

Question : 100 of 150

Marks: +1, -0

(\sqrt[4]{5})^{12}\times (\sqrt{2})^{6}=((2\times 5)^{3})^{x}

is, then what is the value of x?

Solution:

Concept:

Use laws of exponents to simplify each term and compare powers of equal bases.

Explanation:

First, simplify

(\sqrt[4]{5})^{12} = 5^{12/4} = 5^{3}

Next,

(\sqrt{2})^{6} = 2^{6/2} = 2^{3}

Multiply them:

5^{3} \times 2^{3} = (2 \times 5)^{3} = 10^{3}

The right side is

((2 \times 5)^{3})^{x} = (10^{3})^{x} = 10^{3x}

Equate both sides:

10^{3} = 10^{3x}

Since bases are equal, set exponents equal:

3 = 3x

, so

x = 1

Answer:

B. 1

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