Question

$( {3}^{2} )^{6} \times ( {3}^{2} ) ^{2} \times ( {3}^{ - 2} ) ^{10}$

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Answer 1

Answer:

$\frac{1}{81}$

Step-by-step explanation:

$(3^2)^6$ × $(3^2)^2$ × $(3^{-2})^{10$

$=3^{12$ × $3^4$ × $3^{-20$ $($∵ $(a^m)^n=a^{mn})$

⇒ $3^{12+4}$  × $3^{-20$ $($∵ $a^m$ × $a^n=a^{m+n})$

⇒ $3^{16}$  × $3^{-20$

⇒ $3^{-4}$   $($∵ $a^m$ × $a^n=a^{m+n})$

⇒ $\frac{1}{3^4}$ $($∵ $a^{-m}=\frac{1}{a^m} )$

⇒ $\frac{1}{81}$

∴ $(3^2)^6$ × $(3^2)^2$ × $(3^{-2})^{10}=\frac{1}{81}$.

Answer 2

Answer:

${3}^{ - 4}$

Step By Step Explanation:

${3}^{12} + {3}^{4} + {3}^{ - 20} \\ = {3}^{12 + 4 + ( - 20)} \\ = {3}^{12 + 4 - 20} \\ = {3}^{16 - 20} \\ = {3}^{ - 4}$

This Your Answer.