Question

if
$\sqrt[n]{a {}^{2} } = b \\ {b}^{2n = what}$
​

Answer 1

$\sqrt[n]{{a}^{2}} = b \\ \\ {a}^{2} = {b}^{n} \\ \\ {a}^{4} = {b}^{2n}$

Therefore, answer is a^4

Answer 2

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \:SOLUTION \: \: \red{ \mid}}}}}}}}$

$\underline{ \bold{ \: \: GIVEN \: : }} \to \: \: \: \: \: \: \bold{ \sqrt[n]{a {}^{2} } = b } \\ \\ \underline{ \bold{ \: \: TO \: \: FIND \: : }} \to \: \: \: \bold{b {}^{2n} = ? }$

$\underline{ \bold{ \: \: We \: \: know \: \: that \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bold{ \: \: \sqrt[m]{x} = x {}^{ \frac{1}{m} } \: \: }}$

$\underline{ \bold{ \: \: Using \: \: this \: \: formula \: \: }} \\ \\ \: \: \: \: \: \: \: \: \bold{ \sqrt[n]{a {}^{2} } = b} \\ \\ \bold{ \Longrightarrow \: \: (a {}^{2}) {}^{ \frac{1}{n} } = b} \\ \\ \bold{ \Longrightarrow \: \: a {}^{ \frac{2}{n} } = b \: \: \: \: - - - - - > (1)}$

$\bold{Now,} \\ \\ \underline{ \bold{ \: \: Putting \: \: the \: \: value \: \: of \: \: \red{b} \: \: from \: \: (1) \: \: }} \\ \\ \\ \: \: \: \: \: \: \bold{b {}^{2n} =( a {}^{ \frac{2}{n} } ) {}^{2n} } \\ \\ \bold{ \Longrightarrow \: \: b {}^{2n} = (a {}^{ \frac{2}{ \cancel{n}} } ) {}^{2 \: \cancel{n}} } \\ \\ \bold{ \Longrightarrow \: \: b {}^{2n} =( a {}^{2} ) {}^{2} } \\ \\ \bold{ \: \: \: \: \: \: \: \therefore \: \: \boxed{ \bold{b {}^{2n} = a {}^{4} }}}$