Simplify 11x^3*7x^(7/3)

$11 x^{3} \cdot 7 x^{\frac{7}{3}}$

Step 1

Rewrite using the commutative property of multiplication.

$11 \cdot 7 x^{3} x^{\frac{7}{3}}$

Step 2

Multiply $x^{3}$ by $x^{\frac{7}{3}}$ by adding the exponents.

Move $x^{\frac{7}{3}}$ .

$11 \cdot 7 (x^{\frac{7}{3}} x^{3})$

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

$11 \cdot 7 x^{\frac{7}{3} + 3}$

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

$11 \cdot 7 x^{\frac{7}{3} + 3 \cdot \frac{3}{3}}$

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

$11 \cdot 7 x^{\frac{7}{3} + \frac{3 \cdot 3}{3}}$

Combine the numerators over the common denominator.

$11 \cdot 7 x^{\frac{7 + 3 \cdot 3}{3}}$

Simplify the numerator.

Multiply $3$ by $3$ .

$11 \cdot 7 x^{\frac{7 + 9}{3}}$

Add $7$ and $9$ .

$11 \cdot 7 x^{\frac{16}{3}}$

Step 3

Multiply $11$ by $7$ .

$77 x^{\frac{16}{3}}$