Question

The value of m for which \[\left[ \left\{ \left( \frac{1}{7^2} \right)^{- 2} \right\}^{- 1/3} \right]^{1/4} = 7^m ,\] is

Options

• \[- \frac{1}{3}\]

• \[\frac{1}{4}\]

• -3

• 2

Answer 1

We have to find the value of m for  \[\left[ \left\{ \left( \frac{1}{7^2} \right)^{- 2} \right\}^{- 1/3} \right]^{1/4} = 7^m ,\]

⇒ `[{1/(7^(2x-2))}^-1/3]^(1/4) = 7^m`

⇒ `[{1/(7^-4)}^(-1/3)]^(1/4) = 7^m`

⇒ `[{1/(7^(-4x(-1)/3)) }}^(1/4)= 7^m`

⇒ `[{1/(7^(4/3))}]^)1/4 = 7^m`

⇒ `[{1/(7^(4/3 xx1/4))}]  = 7^m`

⇒ `[{1/(7^(4/3 xx1/4))}]  = 7^m`

⇒ `[1/(7^(1/3))] = 7^m`

By using rational exponents  `1/a^n = a^-n`

\[7^\frac{- 1}{3} = 7^m\]

Equating power of exponents we get  `- 1/3 = m`