Franco Avila

2023-03-11

How to simplify ${\left(81\right)}^{\frac{3}{4}}$?

Paxton Houston

Beginner2023-03-12Added 5 answers

Step $1$ :We need find factors of $81$.

$81$can be written as:

$81=3\times 3\times 3\times 3$

$81={3}^{4}$

Step $2$ : Simplify the required term.

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

Using the exponents' law

${\left({3}^{4}\right)}^{\frac{3}{4}}$ can be written as ${3}^{\frac{4\times 3}{4}}$. Thus,

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

${\left(81\right)}^{\frac{3}{4}}=27$.

Hence, ${\left(81\right)}^{\frac{3}{4}}$can be simplified as $27$.

$81$can be written as:

$81=3\times 3\times 3\times 3$

$81={3}^{4}$

Step $2$ : Simplify the required term.

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

Using the exponents' law

${\left({3}^{4}\right)}^{\frac{3}{4}}$ can be written as ${3}^{\frac{4\times 3}{4}}$. Thus,

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

${\left(81\right)}^{\frac{3}{4}}=27$.

Hence, ${\left(81\right)}^{\frac{3}{4}}$can be simplified as $27$.