Arrange the following in increasing order of their values.
A. 16^0.32 × 4^0.36
B. (1/25) [8^1/3 + 27^1/3]²
C. (1024)^−1/5
D. (8/125)^−1/3
Choose the correct answer from the options given below:निम्नलिखित को उनके मानों के बढ़ते क्रम में व्यवस्थित कीजिए।
A. 16^0.32 × 4^0.36
B. (1/25) [8^1/3 + 27^1/3]²
C. (1024)^−1/5
D. (8/125)^−1/3
नीचे दिए गए विकल्पों में से सही उत्तर चुनिए:

1. AB < D < A < C
2. BB < C < D < A
3. CC < D < B < A
4. DC < B < D < A

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: D. C < B < D < A

Explanation

A = 2^4(0.32) × 2^2(0.36) = 2^1.28+0.72 = 2² = 4. B = (1/25)(2 + 3)² = 25/25 = 1. C = (4⁵)^−1/5 = 1/4 = 0.25. D = (125/8)^1/3 = 5/2 = 2.5. Increasing order: 0.25 < 1 < 2.5 < 4, i.e. C < B < D < A.A = 2^4(0.32) × 2^2(0.36) = 2^1.28+0.72 = 2² = 4। B = (1/25)(2 + 3)² = 25/25 = 1। C = (4⁵)^−1/5 = 1/4 = 0.25। D = (125/8)^1/3 = 5/2 = 2.5। बढ़ता क्रम: 0.25 < 1 < 2.5 < 4, अर्थात् C < B < D < A।