Question

Express 81^-2 in power of 3.​

Answer 1

=81^2

=(3^4)^2

=3^8

mark it brainliest.

Answer 2

Given:

$81^{-2}$

We have to express the value of $81^{-2}$ in power of 3.

Solution:

∴ $81^{-2}$

81 = 3 × 3 ×  3 × 3 = $3^{4}$

$81^{-2}$ = $(3^{4} )^{-2}$

Using the exponential identity:

$(a^{m} )^{n}$ = $a^{mn}$

⇒  $81^{-2}$ = $3^{4\times (-2)}$

⇒ $81^{-2}$ = $3^{-8}$

Using the exponential identity:

$a^{-m}$ = $\dfrac{1}{a^m}$

⇒ $81^{-2}$ = $\dfrac{1}{3^8}$

∴ The value of $81^{-2}$ in power of 3 = $3^{-8}$ or $\dfrac{1}{3^8}$

Thus, the value of $81^{-2}$ in power of 3 is "$3^{-8}$ or $\dfrac{1}{3^8}$".