Simplify: {(0.3)^{0}-(0.1)^{-1}}{({3}{2^{4}})^{-1}× (3/2)³-(1/3)^{-1}}

Correct Answer is : −35-3/5−53

Correct Answer is : −35-3/5−53

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Telangana TET Paper 2 Math and Science Model Paper 3

Section: Math and Science

Question : 136 of 150

Marks: +1, -0

Simplify:

\frac{(0.3)^{0}-(0.1)^{-1}}{(\frac{3}{2^{4}})^{-1}\times (\frac{3}{2})^{3}-(\frac{1}{3})^{-1}}

Solution:

Concept:

Any non-zero number raised to power 0 equals 1. A number raised to power −1 equals its reciprocal.

Explanation:

Step 1: Simplify numerator.

(0.3)^0=1

(0.1)^{-1}= \frac{1}{0.1}=10

. So numerator =

1-10=-9

Step 2: Simplify denominator term by term. First term:

(\frac{3}{2^4})^{-1} = \frac{2^4}{3} = \frac{16}{3}

. Second term:

(\frac{3}{2})^3 = \frac{27}{8}

. Their product:

\frac{16}{3} \times \frac{27}{8} = \frac{16 \times 27}{3 \times 8} = \frac{432}{24} = 18

Step 3: Third term:

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

. So denominator becomes

18 - 3 = 15

Step 4: The fraction is

\frac{-9}{15} = -\frac{3}{5}

Answer:

Option B:

-\frac{3}{5}

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