Which of the following is not equal to [(5/6)^1/5]^-1/6
a. (5/6)^{1/5 - 1/6}
b. 1/ [(5/6)^1/5]^1/6
c. (6/5)^1/30
d. (5/6)^-1/30

Solution:

It is given that

\([(\frac{5}{6})^{1/5}]^{-1/6}\)

From the identity a^m × aⁿ = a^{m + n}

= \(\frac{1}{[(\frac{5}{6})^{1/5}]^{1/6}}\)

Taking LCM

= \(\frac{1}{(\frac{5}{6})^{1/30}}\)

= \(\frac{5}{6}^{-1/30}\)

= \((\frac{6}{5})^{1/30}\)

Therefore, \(\frac{5}{6}^{1/5 - 1/6}\) is not equal to \([(\frac{5}{6})^{1/5}]^{-1/6}\).

✦ Try This: Which of the following is not equal to \([(\frac{4}{5})^{1/5}]^{-1/6}\)

a. \(\frac{4}{5}^{1/5 - 1/6}\)

b. \(\frac{1}{[(\frac{4}{5})^{1/5}]^{1/6}}\)

c. \((\frac{5}{4})^{1/30}\)

d. \((\frac{4}{5})^{-1/30}\)

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

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NCERT Exemplar Class 9 Maths Exercise 1.1 Sample Problem 1

Which of the following is not equal to [(5/6)^1/5]^-1/6 a. (5/6)^{1/5 - 1/6}, b. 1/ [(5/6)^1/5]^1/6, c. (6/5)^1/30, d. (5/6)^-1/30

Summary:

All rational numbers and all irrational numbers together make the collection of real numbers. [(5/6)^1/5]^-1/6 is not equal to (5/6)^{1/5 - 1/6}

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• Every rational number is a. a natural number, b. an integer, c. a real number, d. a whole number
• Between two rational numbers a. there is no rational number, b. there is exactly one rational number . . . .
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