Question

Simplify the following expression.

\(\left(\frac{4^{-2}\times3^2}{4\times3^{-4}}\right)^{\frac{1}{3}}\times\frac{4^{-3}\times3^3}{4^{-4}\times3^6}\)

1. \(\frac{1}{9}\)
2. \(\frac{1}{12}\)
3. \(\frac{1}{3}\)
4. \(\frac{27}{16}\)

Answer 1

Correct Answer - Option 3 : \(\frac{1}{3}\)

Formula used:

a^m/aⁿ = a^{(m - n)}

a^-1 = 1/a

a⁰ = 1

Calculation:

\(\left(\frac{4^{-2}×3^2}{4×3^{-4}}\right)^{\frac{1}{3}}×\frac{4^{-3}×3^3}{4^{-4}×3^6}\)

⇒  \(({4^{-3}×3^{6}})^{\frac{1}{3}} × 4^{1} × 3^{- 3}\)

⇒ \({4^{-1}×3^{2}} × 4^{1} × 3^{- 3}\)

⇒ 4⁰ × 3^{- 1}

⇒ 1 × 1/3 = 1/3

∴ The required will be 1/3.