Simplify (3x^5)(4x^(5/6))

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

Step 1

Rewrite using the commutative property of multiplication.

$3 \cdot 4 x^{5} x^{\frac{5}{6}}$

Step 2

Multiply $x^{5}$ by $x^{\frac{5}{6}}$ by adding the exponents.

Move $x^{\frac{5}{6}}$ .

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

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

$3 \cdot 4 x^{\frac{5}{6} + 5}$

To write $5$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$3 \cdot 4 x^{\frac{5}{6} + 5 \cdot \frac{6}{6}}$

Combine $5$ and $\frac{6}{6}$ .

$3 \cdot 4 x^{\frac{5}{6} + \frac{5 \cdot 6}{6}}$

Combine the numerators over the common denominator.

$3 \cdot 4 x^{\frac{5 + 5 \cdot 6}{6}}$

Simplify the numerator.

Multiply $5$ by $6$ .

$3 \cdot 4 x^{\frac{5 + 30}{6}}$

Add $5$ and $30$ .

$3 \cdot 4 x^{\frac{35}{6}}$

Step 3

Multiply $3$ by $4$ .

$12 x^{\frac{35}{6}}$