Simplify (3^(2/3)*5^(1/4))^6

${(3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}})}^{6}$

Step 1

Apply the product rule to $3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}}$ .

${(3^{\frac{2}{3}})}^{6} \cdot {(5^{\frac{1}{4}})}^{6}$

Step 2

Multiply the exponents in ${(3^{\frac{2}{3}})}^{6}$ .

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

$3^{\frac{2}{3} \cdot 6} \cdot {(5^{\frac{1}{4}})}^{6}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$3^{\frac{2}{3} \cdot (3 (2))} \cdot {(5^{\frac{1}{4}})}^{6}$

Cancel the common factor.

$3^{\frac{2}{3} \cdot (3 \cdot 2)} \cdot {(5^{\frac{1}{4}})}^{6}$

Rewrite the expression.

$3^{2 \cdot 2} \cdot {(5^{\frac{1}{4}})}^{6}$

Multiply $2$ by $2$ .

$3^{4} \cdot {(5^{\frac{1}{4}})}^{6}$

Step 3

Raise $3$ to the power of $4$ .

$81 \cdot {(5^{\frac{1}{4}})}^{6}$

Step 4

Multiply the exponents in ${(5^{\frac{1}{4}})}^{6}$ .

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

$81 \cdot 5^{\frac{1}{4} \cdot 6}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$81 \cdot 5^{\frac{1}{2 (2)} \cdot 6}$

Factor $2$ out of $6$ .

$81 \cdot 5^{\frac{1}{2 \cdot 2} \cdot (2 \cdot 3)}$

Cancel the common factor.

$81 \cdot 5^{\frac{1}{2 \cdot 2} \cdot (2 \cdot 3)}$

Rewrite the expression.

$81 \cdot 5^{\frac{1}{2} \cdot 3}$

Combine $\frac{1}{2}$ and $3$ .

$81 \cdot 5^{\frac{3}{2}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$81 \cdot 5^{\frac{3}{2}}$

Decimal Form:

$905.60753088 \dots$