Simplify 2m^2(4m^(3/2))(4m^-2)

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

Step 1

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

Move $m^{\frac{3}{2}}$ .

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

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

$2 m^{\frac{3}{2} + 2} \cdot 4 \cdot (4 m^{- 2})$

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

$2 m^{\frac{3}{2} + 2 \cdot \frac{2}{2}} \cdot 4 \cdot (4 m^{- 2})$

Combine $2$ and $\frac{2}{2}$ .

$2 m^{\frac{3}{2} + \frac{2 \cdot 2}{2}} \cdot 4 \cdot (4 m^{- 2})$

Combine the numerators over the common denominator.

$2 m^{\frac{3 + 2 \cdot 2}{2}} \cdot 4 \cdot (4 m^{- 2})$

Simplify the numerator.

Multiply $2$ by $2$ .

$2 m^{\frac{3 + 4}{2}} \cdot 4 \cdot (4 m^{- 2})$

Add $3$ and $4$ .

$2 m^{\frac{7}{2}} \cdot 4 \cdot (4 m^{- 2})$

Step 2

Multiply $m^{\frac{7}{2}}$ by $m^{- 2}$ by adding the exponents.

Move $m^{- 2}$ .

$2 (m^{- 2} m^{\frac{7}{2}}) \cdot 4 \cdot 4$

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

$2 m^{- 2 + \frac{7}{2}} \cdot 4 \cdot 4$

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

$2 m^{- 2 \cdot \frac{2}{2} + \frac{7}{2}} \cdot 4 \cdot 4$

Combine $- 2$ and $\frac{2}{2}$ .

$2 m^{\frac{- 2 \cdot 2}{2} + \frac{7}{2}} \cdot 4 \cdot 4$

Combine the numerators over the common denominator.

$2 m^{\frac{- 2 \cdot 2 + 7}{2}} \cdot 4 \cdot 4$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$2 m^{\frac{- 4 + 7}{2}} \cdot 4 \cdot 4$

Add $- 4$ and $7$ .

$2 m^{\frac{3}{2}} \cdot 4 \cdot 4$

Step 3

Multiply $4$ by $2$ .

$8 m^{\frac{3}{2}} \cdot 4$

Step 4

Multiply $4$ by $8$ .

$32 m^{\frac{3}{2}}$

Simplify 2m^2*(4m^(3/2))*(4m^-2)