Question

which of the following is equals to X ?
(a) x^12/17-x^5/7
(b) 12√(x^4)^1/3
(c) (√x^3)^2/3
(d) x^12/7*x^7/12


please send me with full solution.

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Answer 1

(c) (√x^3)^2/3 will be the answer.

(√x^3)^2/3 = (x∧(3/2))∧2/3 = x∧(3/2*2/3) = x∧1 = x

Answer 2

Option 'c' is correct.

Step-by-step explanation:

Since we have given that

(a) $x^{\frac{12}{17}}-x^{\frac{5}{7}$

(b) $12\sqrt{(x^4)}^{\frac{1}{3}}=12x^{\frac{4}{2}\times \frac{1}{3}}=12x^{\frac{2}{3}}$

(c) $(\sqrt{x^3}^{\frac{2}{3}})=x^{\frac{1}{2}\times \frac{2}{3}\times 3}=x$

(d) $x^{\frac{12}{7}}\times x^{\frac{7}{12}}=x^{\frac{7}{12}+\frac{12}{7}}=x^{\frac{49+144}{7}}=x^{\frac{193}{7}}$

Hence, only third expression is equals to x.

Therefore, Option 'c' is correct.

# learn more:

1. Decimal representation of a rational number can not be

(a) Terminating (b) Non terminating (c) Non Terminating & Repeating (d) Non terminating non repeating

2. The product of any two irrational is

(a) Always a irrational number (b) Always a rational number

(c) Always an integer (d) Sometimes rational , sometimes irrational

3. Which of the following is equal to x?

(a) x12/7-x5/7 (b) (x4)1/3 (c) (x3/2 )2/3

4. The value of √34 + √48 ÷ √8 + √12 is equal to

(a) 2 (b) √2 (c) 4 (d) 8

5. The value of ((22)1/3)1/4 is

(a) 2-1/6 (b) 2-6 (c) 21/6 (d) 26

6. Express 0.003232323232...... in the form of P/Q.

7.. Write the following in decimal form and what kind of decimal expansion each has?

(a) 2/15 (b) 329/500

8. Simplify (√3 – √5) (√ 5 + √3) / 7-2 √5

9. If x = 1+ √2, then find the value of (x-1/x)3

10. If x = √ 3 +√ 2 / √3 –√ 2 and y =√ 3 – √2 / √3 +√ 2, find the value of( x+y)2

11. If 3 + √7 / 3 – √7 = a + b √7, find the value of a & b.

12. Find the value of [ (16)1/2 ]1/2

13. Simplify ( 81/16)-3/4 * [(9/25)3/2 ÷ (5/2)-3 ]

14. Find the value of X , if (6/5)x (5/6)2x = 125/216

15. Show that (xa-b)a+b .(xb-c)b+c .(xc-a)c+a = 1

16. Simplify the expression [(3/5)1/4]-1/5

17. If x = 3 + √8 , find the value of (x2 + 1/ x2 )

18. Find five rational numbers between 4/5 and 5/6

19. Express 32.1235 in the form of P/Q

20. Draw √6 on a number line​

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