Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $2$ by $2$ .

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

Step 1.6.2

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.

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Step 2.1

Move $m^{- 2}$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 2$ by $2$ .

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

Step 2.6.2

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 $8$ .

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