13√13 × 133 ÷ 13-3/2 = 13q+4, find the value of q.1. 42. 33. 24. 1

1.	13√13 × 133 ÷ 13-3/2 = 13q+4, find the value of q.1. 42. 33. 24. 1
Answer» Correct Answer - Option 3 : 2 Given∶ 13√13 × 13³ ÷ 13^-3/2 = 13^{q + 4} Formula Used∶ ^m√a = (a)^1/m, a^m × aⁿ = a^{m + n} When x^a = x^b, then a = b Calculation∶ [13. (13)^1/2 × 13³]/(13)^-3/2 = 13^{q + 4} ⇒ 13^{1 + (1/2) + 3}. 13^3/2 = 13^q+4 ⇒ 13^{1 + (1/2) + 3 + (3/2)} = 13^{q + 4} ⇒ 13⁶ =13^{q + 4} ⇒ q + 4 = 6 ⇒ q = 6 – 4 = 2 ∴ The value of q is 2.

Answer» Correct Answer - Option 3 : 2

Given∶

13√13 × 13³ ÷ 13^-3/2 = 13^{q + 4}

Formula Used∶

^m√a = (a)^1/m, a^m × aⁿ = a^{m + n}

When x^a = x^b, then a = b

Calculation∶

[13. (13)^1/2 × 13³]/(13)^-3/2 = 13^{q + 4}

⇒ 13^{1 + (1/2) + 3}. 13^3/2 = 13^q+4

⇒ 13^{1 + (1/2) + 3 + (3/2)} = 13^{q + 4}

⇒ 13⁶ =13^{q + 4}

⇒ q + 4 = 6

⇒ q = 6 – 4 = 2

∴ The value of q is 2.

Discussion