Answered

From science to arts, IDNLearn.com has the answers to all your questions. Get accurate and detailed answers to your questions from our knowledgeable and dedicated community members.

Convert the following expression to simplify faction or integer. If it is not a real number, enter None

Convert The Following Expression To Simplify Faction Or Integer If It Is Not A Real Number Enter None class=

Sagot :

Given an expression:

[tex]81^{-\frac{1}{4}}[/tex]

We have to simplify the given expression.

We know that:

[tex]x^{-a}=\frac{1}{x^a}[/tex]

So,

[tex]81^{-\frac{1}{4}}=\frac{1}{81^{\frac{1}{4}}}[/tex]

Let:

[tex]\begin{gathered} x=\frac{1}{81^{\frac{1}{4}}} \\ \Rightarrow x^4=(\frac{1}{81^{\frac{1}{4}}})^4 \\ \Rightarrow x^4=\frac{1}{81} \\ \Rightarrow x^4=(\frac{1}{3})^4 \\ \Rightarrow x=\frac{1}{3} \end{gathered}[/tex]

Thus, the answer is 1/3.

We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.