Simplify [{(1/3)^{-3}-(1/4)^{-2}}÷ (1/4)^{-3}]

Correct Answer is : 116411/646411

Correct Answer is : 116411/646411

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UPTET Paper 1 2022 Solved Paper

Question : 93 of 150

Marks: +1, -0

Simplify

[{(\frac{1}{3})^{-3}-(\frac{1}{4})^{-2}}\div (\frac{1}{4})^{-3}]

Solution:

Concept:

Use the property

a^{-n} = \frac{1}{a^n}

to rewrite negative exponents as positive powers, then simplify the expression step by step.

Explanation:

First, rewrite each term:

(\frac{1}{3})^{-3} = 3^3 = 27

(\frac{1}{4})^{-2} = 4^2 = 16

, and

(\frac{1}{4})^{-3} = 4^3 = 64

Now substitute:

[27 - 16] \div 64 = 11 \div 64 = \frac{11}{64}

Answer:

\frac{11}{64}

, which matches option A.

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