Question

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

Answer 1

Step $1$ : 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 law of exponents

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