Simplify (7x^(1/3))(2x^(1/4))

$(7 x^{\frac{1}{3}}) (2 x^{\frac{1}{4}})$

Step 1

Rewrite using the commutative property of multiplication.

$7 \cdot 2 x^{\frac{1}{3}} x^{\frac{1}{4}}$

Step 2

Multiply $x^{\frac{1}{3}}$ by $x^{\frac{1}{4}}$ by adding the exponents.

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

$7 \cdot 2 (x^{\frac{1}{4}} x^{\frac{1}{3}})$

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

$7 \cdot 2 x^{\frac{1}{4} + \frac{1}{3}}$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$7 \cdot 2 x^{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3}}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$7 \cdot 2 x^{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4}}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$7 \cdot 2 x^{\frac{3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4}}$

Multiply $4$ by $3$ .

$7 \cdot 2 x^{\frac{3}{12} + \frac{1}{3} \cdot \frac{4}{4}}$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$7 \cdot 2 x^{\frac{3}{12} + \frac{4}{3 \cdot 4}}$

Multiply $3$ by $4$ .

$7 \cdot 2 x^{\frac{3}{12} + \frac{4}{12}}$

Combine the numerators over the common denominator.

$7 \cdot 2 x^{\frac{3 + 4}{12}}$

Add $3$ and $4$ .

$7 \cdot 2 x^{\frac{7}{12}}$

Step 3

Multiply $7$ by $2$ .

$14 x^{\frac{7}{12}}$