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

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Multiply $x^{\frac{2}{3}}$ by $x^{\frac{3}{4}}$ by adding the exponents.

Move $x^{\frac{3}{4}}$ .

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

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

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

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

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

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

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

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

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

Multiply $4$ by $3$ .

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

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

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

Multiply $3$ by $4$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $3$ .

$3 \cdot 4 x^{\frac{9 + 2 \cdot 4}{12}}$

Multiply $2$ by $4$ .

$3 \cdot 4 x^{\frac{9 + 8}{12}}$

Add $9$ and $8$ .

$3 \cdot 4 x^{\frac{17}{12}}$

Step 3

Multiply $3$ by $4$ .

$12 x^{\frac{17}{12}}$