Question

How do you simplify $8^{\frac{3}{4}}$ ?

Answer 1

Step $1$ : Find factors of $8$.

$8$ can be written as:

$8=2\times 2\times 2$

$8=2^3$

Step $2$ : Simplify the required term.

$8^{\frac{3}{4}}$$={\left(2^3\right)}^{\frac{3}{4}}$

Using the law of exponents,

${\left(2^3\right)}^{\frac{3}{4}}$ can be written as $2^{\frac{3\times 3}{4}}$. Thus,

${\left(8\right)}^{\frac{3}{4}}$$=2^{\frac{9}{4}}$.

Hence, ${\left(8\right)}^{\frac{3}{4}}$ can be simplified as $2^{\frac{9}{4}}$.