Test Index

CTET Paper II (Mathematics and Science) 29 Jan 2023 Solved Paper

© examsnet.com

Question : 34 of 150

Marks: +1, -0

\frac{(27)^{4}}{(125)^{2}}÷{(\frac{5}{9})^{-2}(\frac{3}{5})^{6}}

is equal to :

125
225
289
300

Solution:

Concept:

Convert all terms into prime factors and simplify the division by multiplying with the reciprocal.

Explanation:

Write

27

as

3^3

and

125

as

5^3

. Then

(27)^4 = (3^3)^4 = 3^{12}

and

(125)^2 = (5^3)^2 = 5^6

. So the first part is

\frac{3^{12}}{5^6}

.

The denominator:

(\frac{5}{9})^{-2} = (\frac{9}{5})^2 = \frac{9^2}{5^2} = \frac{3^4}{5^2}

. Also

(\frac{3}{5})^6 = \frac{3^6}{5^6}

. Multiply these:

\frac{3^4}{5^2} \times \frac{3^6}{5^6} = \frac{3^{10}}{5^8}

.

Now divide:

\frac{3^{12}}{5^6} \div \frac{3^{10}}{5^8} = \frac{3^{12}}{5^6} \times \frac{5^8}{3^{10}} = 3^{12-10} \times 5^{8-6} = 3^2 \times 5^2 = 9 \times 25 = 225

.

Answer:

225 (Option B)

© examsnet.com

Go to Question:

Prev Question

Next Question