Franco Avila

2023-03-11

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

Paxton Houston

Step $1$ :We need find factors of $81$.
$81$can be written as:
$81=3×3×3×3$
$81={3}^{4}$
Step $2$ : Simplify the required term.
${\left(81\right)}^{\frac{3}{4}}$$={\left({3}^{4}\right)}^{\frac{3}{4}}$
Using the exponents' law
${\left({3}^{4}\right)}^{\frac{3}{4}}$ can be written as ${3}^{\frac{4×3}{4}}$. Thus,
${\left(81\right)}^{\frac{3}{4}}$$={3}^{3}$
${\left(81\right)}^{\frac{3}{4}}=27$.
Hence, ${\left(81\right)}^{\frac{3}{4}}$can be simplified as $27$.

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