Question

Find x, if \({\left( {\frac{2}{3}} \right)^{ - 5}} \times {\left( {\frac{2}{3}} \right)^{ - 11}} = {\left( {\frac{2}{3}} \right)^{8x}}\)
1. -2
2. 3
3. 2
4. -3

Answer 1

Correct Answer - Option 1 : -2

Given:

\((\frac{2}{3})^{-5} × (\frac{2}{3})^{-11} = (\frac{2}{3})^{8x}\)

Concept Used:

a^m × aⁿ = a^{m + n}

If a^m = aⁿ, then m = n 

Calculation:

\((\frac{2}{3})^{-5} × (\frac{2}{3})^{-11} = (\frac{2}{3})^{8x}\)

⇒ \((\frac{2}{3})^{-16} = (\frac{2}{3})^{8x}\)

⇒ 8x = -16

∴ The value of 'x' is  -2