Simplify 2b^(-1/4)*3b^(-3/2)

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Multiply $b^{- \frac{1}{4}}$ by $b^{- \frac{3}{2}}$ by adding the exponents.

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

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

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

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

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

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

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 3$ by $2$ .

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

Subtract $1$ from $- 6$ .

$2 \cdot 3 b^{\frac{- 7}{4}}$

Move the negative in front of the fraction.

$2 \cdot 3 b^{- \frac{7}{4}}$

Step 3

Multiply $2$ by $3$ .

$6 b^{- \frac{7}{4}}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$6 \frac{1}{b^{\frac{7}{4}}}$

Step 5

Combine $6$ and $\frac{1}{b^{\frac{7}{4}}}$ .

$\frac{6}{b^{\frac{7}{4}}}$