Simplify (b^3)/(c^(1/2))*c/(b^(1/3))

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

Combine.

$\frac{b^{3} c}{c^{\frac{1}{2}} b^{\frac{1}{3}}}$

Move $b^{\frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{b^{3} c b^{- \frac{1}{3}}}{c^{\frac{1}{2}}}$

Move $c^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$b^{3} c b^{- \frac{1}{3}} c^{- \frac{1}{2}}$

Multiply $b^{3}$ by $b^{- \frac{1}{3}}$ by adding the exponents.

Move $b^{- \frac{1}{3}}$ .

$b^{- \frac{1}{3}} b^{3} c \cdot c^{- \frac{1}{2}}$

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $3$ .

$b^{\frac{- 1 + 9}{3}} c \cdot c^{- \frac{1}{2}}$

Add $- 1$ and $9$ .

$b^{\frac{8}{3}} c \cdot c^{- \frac{1}{2}}$

Multiply $c$ by $c^{- \frac{1}{2}}$ by adding the exponents.

Move $c^{- \frac{1}{2}}$ .

$b^{\frac{8}{3}} (c^{- \frac{1}{2}} c)$

Multiply $c^{- \frac{1}{2}}$ by $c$ .

Raise $c$ to the power of $1$ .

$b^{\frac{8}{3}} (c^{- \frac{1}{2}} c^{1})$

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

$b^{\frac{8}{3}} c^{- \frac{1}{2} + 1}$

Write $1$ as a fraction with a common denominator.

$b^{\frac{8}{3}} c^{- \frac{1}{2} + \frac{2}{2}}$

Combine the numerators over the common denominator.

$b^{\frac{8}{3}} c^{\frac{- 1 + 2}{2}}$

Add $- 1$ and $2$ .

$b^{\frac{8}{3}} c^{\frac{1}{2}}$