Given:
[tex](\sqrt[4]{81})^{5}[/tex]
To find:
Exponential form
Simplified form
Solution:
[tex](\sqrt[4]{81})^{5}[/tex]
Apply radical rule:
[tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
[tex](\sqrt[4]{81})^{5}=\left(81^{\frac{1}{4}}\right)^{5}[/tex]
Apply exponent rule:
[tex]\left(a^{b}\right)^{c}=a^{b c}[/tex]
[tex]$\left(81^{\frac{1}{4}}\right)^{5}=81^{\frac{5}{4}}[/tex]
The exponent form of [tex](\sqrt[4]{81})^{5}[/tex] is [tex]81^{\frac{5}{4}}[/tex].
Factor the number [tex]81=3^{4}[/tex]
[tex]81^{\frac{5}{4}}=\left(3^{4}\right)^{\frac{5}{4}}[/tex]
Both 4 in the numerator and denominator of powers get canceled.
[tex]=3^{5}[/tex]
= 243
The simplified form is 243.
