Simplify ((b^(3/2))/(b^(2/3)))

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

Step 1

Remove parentheses.

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

Step 2

Move $b^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 3

Multiply $b^{\frac{3}{2}}$ by $b^{- \frac{2}{3}}$ by adding the exponents.

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

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

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

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

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

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

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

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

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

Multiply $2$ by $3$ .

$b^{\frac{3 \cdot 3}{6} - \frac{2}{3} \cdot \frac{2}{2}}$

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

$b^{\frac{3 \cdot 3}{6} - \frac{2 \cdot 2}{3 \cdot 2}}$

Multiply $3$ by $2$ .

$b^{\frac{3 \cdot 3}{6} - \frac{2 \cdot 2}{6}}$

Combine the numerators over the common denominator.

$b^{\frac{3 \cdot 3 - 2 \cdot 2}{6}}$

Simplify the numerator.

Multiply $3$ by $3$ .

$b^{\frac{9 - 2 \cdot 2}{6}}$

Multiply $- 2$ by $2$ .

$b^{\frac{9 - 4}{6}}$

Subtract $4$ from $9$ .

$b^{\frac{5}{6}}$