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Q4. What is the value of [tex]\(\sqrt[4]{(81)^{-2}}\)[/tex]?
a. [tex]\(\frac{1}{9}\)[/tex] b. [tex]\(\frac{1}{3}\)[/tex] c. 9 d. [tex]\(\frac{1}{81}\)[/tex]
To solve the given problem, we need to find the value of [tex]\(\sqrt[4]{(81)^{-2}}\)[/tex].
Let's proceed step-by-step:
1. Evaluate the exponentiation [tex]\((81)^{-2}\)[/tex]: - When a number is raised to a power of [tex]\(-n\)[/tex], it’s equivalent to the reciprocal of that number raised to the power [tex]\(n\)[/tex]. Thus, we have: [tex]\[
(81)^{-2} = \frac{1}{81^2}
\][/tex]
2. Calculate [tex]\(81^2\)[/tex]: - [tex]\(81\)[/tex] is [tex]\(9^2\)[/tex] and [tex]\((9^2)^2 = 9^4\)[/tex]: [tex]\[
81^2 = 9^4 = 6561
\][/tex]
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