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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
Solution
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`
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