Simplify (2x^(2/5))(6x^(1/4))

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

Step 1

Rewrite using the commutative property of multiplication.

$2 \cdot 6 x^{\frac{2}{5}} x^{\frac{1}{4}}$

Step 2

Multiply $x^{\frac{2}{5}}$ by $x^{\frac{1}{4}}$ by adding the exponents.

Move $x^{\frac{1}{4}}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 6 x^{\frac{1}{4} + \frac{2}{5}}$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 \cdot 6 x^{\frac{1}{4} \cdot \frac{5}{5} + \frac{2}{5}}$

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 \cdot 6 x^{\frac{1}{4} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{4}{4}}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$2 \cdot 6 x^{\frac{5}{4 \cdot 5} + \frac{2}{5} \cdot \frac{4}{4}}$

Multiply $4$ by $5$ .

$2 \cdot 6 x^{\frac{5}{20} + \frac{2}{5} \cdot \frac{4}{4}}$

Multiply $\frac{2}{5}$ by $\frac{4}{4}$ .

$2 \cdot 6 x^{\frac{5}{20} + \frac{2 \cdot 4}{5 \cdot 4}}$

Multiply $5$ by $4$ .

$2 \cdot 6 x^{\frac{5}{20} + \frac{2 \cdot 4}{20}}$

Combine the numerators over the common denominator.

$2 \cdot 6 x^{\frac{5 + 2 \cdot 4}{20}}$

Simplify the numerator.

Multiply $2$ by $4$ .

$2 \cdot 6 x^{\frac{5 + 8}{20}}$

Add $5$ and $8$ .

$2 \cdot 6 x^{\frac{13}{20}}$

Step 3

Multiply $2$ by $6$ .

$12 x^{\frac{13}{20}}$