Question

I hate math when I don’t know how to do it and since I don’t have school well it’s hard for me to understand it thank you for helping.

Answer 1

Given:

$(\sqrt[4]{81})^{5}$

To find:

Exponential form

Simplified form

Solution:

$(\sqrt[4]{81})^{5}$

Apply radical rule:

$\sqrt[n]{a}=a^{\frac{1}{n}}$

$(\sqrt[4]{81})^{5}=\left(81^{\frac{1}{4}}\right)^{5}$

Apply exponent rule:

$\left(a^{b}\right)^{c}=a^{b c}$

$\left(81^{\frac{1}{4}}\right)^{5}=81^{\frac{5}{4}}$

The exponent form of $(\sqrt[4]{81})^{5}$ is $81^{\frac{5}{4}}$.

Factor the number $81=3^{4}$

$81^{\frac{5}{4}}=\left(3^{4}\right)^{\frac{5}{4}}$

Both 4 in the numerator and denominator of powers get canceled.

      $=3^{5}$

      = 243

The simplified form is 243.