Simplify (6^(2/3))^(3/4)

${(6^{\frac{2}{3}})}^{\frac{3}{4}}$

Step 1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$6^{\frac{2}{3} \cdot \frac{3}{4}}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$6^{\frac{2}{3} \cdot \frac{3}{2 (2)}}$

Cancel the common factor.

$6^{\frac{2}{3} \cdot \frac{3}{2 \cdot 2}}$

Rewrite the expression.

$6^{\frac{1}{3} \cdot \frac{3}{2}}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$6^{\frac{1}{3} \cdot \frac{3}{2}}$

Rewrite the expression.

$6^{\frac{1}{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6^{\frac{1}{2}}$

Decimal Form:

$2.44948974 \dots$