Question

If x^y+z = 1, y^{x + z} = 729 and z^{x + y} = 625, then, what is the value of (x + 2)^{y + z + 1}?
1. 19683
2. 19652
3. 19458
4. 16980

Answer 1

Correct Answer - Option 1 : 19683

x^y+z = 1

∴ x = 1

y^{x + z} = 729

⇒ y^{x + z} = 3⁶

∴ y = 3

∴ x + z = 6

⇒ z = 6 – 1

⇒ z = 5

and z^{x + y} = 625

⇒ z^{x + y} = 5⁴

∴ z = 5

According to question-

∴ x = 1, y = 3 & z = 5

(x + 2)^{y + z + 1}

⇒ (1 + 2)^{(3 + 5 + 1)}

⇒ 3⁹

⇒ 19683