The value of m such that \((\frac{2}{9})^3 \times (\frac{4}{81})^{-6}

1.	The value of m such that \((\frac{2}{9})^3 \times (\frac{4}{81})^{-6} = (\frac{2}{9})^{2m-1}\) is1. -42. 33. -64. 0
Answer» Correct Answer - Option 1 : -4 Given: \((\frac{2}{9})^3 \times (\frac{4}{81})^{-6} = (\frac{2}{9})^{2m-1}\) Formula required: \(\sqrt[2]{a} = a^{1/2}\) \(\sqrt[3]{a} = a^{1/n}\) \(a^m \times a^n = a^{m + n}\) a-m = 1/am Calculations: \(\frac{4}{81} = (\frac{2}{9})^2\) [(2/9)²]^-6= (2/9)^-12 \((\frac{2}{9})^3 \times (\frac{2}{9})^{-12} = (\frac{2}{9})^{2m-1}\) ⇒ 3 - 12 = 2m - 1 ⇒ 2m = 3 - 12 + 1 ⇒ 2m = - 8 ⇒ m = - 8/2 Hence, m = - 4 ∴ The value of m is -4

The value of m such that \((\frac{2}{9})^3 \times (\frac{4}{81})^{-6} = (\frac{2}{9})^{2m-1}\) is1. -42. 33. -64. 0

Answer» Correct Answer - Option 1 : -4

Given:

\((\frac{2}{9})^3 \times (\frac{4}{81})^{-6} = (\frac{2}{9})^{2m-1}\)

Formula required:

\(\sqrt[2]{a} = a^{1/2}\)

\(\sqrt[3]{a} = a^{1/n}\)

\(a^m \times a^n = a^{m + n}\)

a-m = 1/am

Calculations:

\(\frac{4}{81} = (\frac{2}{9})^2\)

[(2/9)²]^-6= (2/9)^-12

\((\frac{2}{9})^3 \times (\frac{2}{9})^{-12} = (\frac{2}{9})^{2m-1}\)

⇒ 3 - 12 = 2m - 1

⇒ 2m = 3 - 12 + 1

⇒ 2m = - 8

⇒ m = - 8/2

Hence, m = - 4

∴ The value of m is -4