Find the value of 'x'\({6^2} \times {3^{3x}} = {\left( {27} \right)^{3

1.	Find the value of 'x'\({6^2} \times {3^{3x}} = {\left( {27} \right)^{3x + 2}} \times 4\)1. -3/22. 2/33. -2/34. 3/2
Answer» Correct Answer - Option 3 : -2/3 Formula used: a^m × aⁿ = a^{m + n} (a × b)^m = a^m × b^m Calculation: By using formula ⇒ (2 × 3)² × 3^3x = (3³)^{3x + 2} × 2² ⇒ 2² × 3² × 3^3x = 3^{9x + 6} × 2² ⇒ 3^{3x + 2} = 3^{9x + 6} Now, ccompairing power ⇒ 3x + 2 = 9x + 6 ⇒ 6x = -4 ⇒ x = -4/6 ⇒ x = -2/3 ∴ The required value of 'x' is -2/3.

Find the value of 'x'\({6^2} \times {3^{3x}} = {\left( {27} \right)^{3x + 2}} \times 4\)1. -3/22. 2/33. -2/34. 3/2

Answer» Correct Answer - Option 3 : -2/3

Formula used:

a^m × aⁿ = a^{m + n}

(a × b)^m = a^m × b^m

Calculation:

By using formula

⇒ (2 × 3)² × 3^3x = (3³)^{3x + 2} × 2²

⇒ 2² × 3² × 3^3x = 3^{9x + 6} × 2²

⇒ 3^{3x + 2} = 3^{9x + 6}

Now, ccompairing power

⇒ 3x + 2 = 9x + 6

⇒ 6x = -4

⇒ x = -4/6

⇒ x = -2/3

∴ The required value of 'x' is -2/3.