# 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. [(x^{3})^{1/2 }]^{2/3 }= x^{3/2 × 2/3 }= x^{1 }= x

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

Therefore, [(x^{3})^{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 [(x^{3})^{1/2 }]^{2/3} is equal to x

**☛ Related Questions:**

- Are there two irrational numbers whose sum and product both are rationals? Justify
- There is a number x such that x2 is irrational but x4 is rational. Is the given statement true or fa . . . .
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