Which of the following is equal to x
a. x^12/7 × x^5/7
b. \(\sqrt[12]{(x^{4})^{1/3}}\)
c. \((\sqrt{x^{3}})^{2/3}\)
d. x^12/7 × x^7/12

Solution:

Let us simplify each option

a. x^12/7 × x^5/7≠ x

b. \(\sqrt[12]{(x^{4})^{1/3}}\) = \(\sqrt[12]{x^{4\times 1/3}}\)

It can be written as

= (x^4/3)^1/12

= x^{4/3 × 1/12}

So we get

= x^1/9

≠ x

c. [(x³)^1/2 ]^2/3 = x^{3/2 × 2/3} = x¹ = x

d. x^12/7 × x^7/12 = x^{12/7 + 7/12} = x^193/84 ≠ x

Therefore, [(x³)^1/2 ]^2/3 is equal to x.

✦ Try This: Value of (625)⁰²⁵ × (625)^0.5 is

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

NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 21

Which of the following is equal to x? a. x^12/7 × x^5/7, b. \(\sqrt[12]{(x^{4})^{1/3}}\), c. \((\sqrt{x^{3}})^{2/3}\), d. x^12/7 × x^7/12

Summary:

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. So [(x³)^1/2 ]^2/3 is equal to x

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