Basic Math Examples

$2 m^{\frac{3}{4}} n^{2} \cdot (3 m^{\frac{1}{4}} n)$

Step 1

Multiply $m^{\frac{3}{4}}$ by $m^{\frac{1}{4}}$ by adding the exponents.

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Step 1.1

Move $m^{\frac{1}{4}}$ .

$2 (m^{\frac{1}{4}} m^{\frac{3}{4}}) n^{2} \cdot (3 n)$

Step 1.2

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

$2 m^{\frac{1}{4} + \frac{3}{4}} n^{2} \cdot (3 n)$

Step 1.3

Combine the numerators over the common denominator.

$2 m^{\frac{1 + 3}{4}} n^{2} \cdot (3 n)$

Step 1.4

Add $1$ and $3$ .

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

Step 1.5

Divide $4$ by $4$ .

$2 m^{1} n^{2} \cdot (3 n)$

Step 2

Simplify $2 m^{1} n^{2} \cdot (3 n)$ .

$2 m n^{2} \cdot (3 n)$

Step 3

Multiply $n^{2}$ by $n$ by adding the exponents.

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Step 3.1

Move $n$ .

$2 m (n \cdot n^{2}) \cdot 3$

Step 3.2

Multiply $n$ by $n^{2}$ .

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Step 3.2.1

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

$2 m (n^{1} n^{2}) \cdot 3$

Step 3.2.2

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

$2 m n^{1 + 2} \cdot 3$

Step 3.3

Add $1$ and $2$ .

$2 m n^{3} \cdot 3$

Step 4

Multiply $3$ by $2$ .

$6 m n^{3}$