Simplify the Radical Expression 3b^(1/2)*b^(4/3)

$3 b^{\frac{1}{2}} \cdot b^{\frac{4}{3}}$

Step 1

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

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

Step 2

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

$3 b^{\frac{4}{3} + \frac{1}{2}}$

Step 3

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

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

Step 4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $2$ .

$3 b^{\frac{4 \cdot 2}{6} + \frac{1}{2} \cdot \frac{3}{3}}$

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$3 b^{\frac{4 \cdot 2}{6} + \frac{3}{2 \cdot 3}}$

Multiply $2$ by $3$ .

$3 b^{\frac{4 \cdot 2}{6} + \frac{3}{6}}$

Step 6

Combine the numerators over the common denominator.

$3 b^{\frac{4 \cdot 2 + 3}{6}}$

Step 7

Simplify the numerator.

Multiply $4$ by $2$ .

$3 b^{\frac{8 + 3}{6}}$

Add $8$ and $3$ .

$3 b^{\frac{11}{6}}$