Basic Math Examples

${(2 m n)}^{2} {(4 m n)}^{3}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $2 m n$ .

${(2 m)}^{2} n^{2} {(4 m n)}^{3}$

Step 1.2

Apply the product rule to $2 m$ .

$2^{2} m^{2} n^{2} {(4 m n)}^{3}$

Step 2

Raise $2$ to the power of $2$ .

$4 m^{2} n^{2} {(4 m n)}^{3}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $4 m n$ .

$4 m^{2} n^{2} ({(4 m)}^{3} n^{3})$

Step 3.2

Apply the product rule to $4 m$ .

$4 m^{2} n^{2} (4^{3} m^{3} n^{3})$

Step 4

Multiply $4$ by $4^{3}$ by adding the exponents.

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Step 4.1

Move $4^{3}$ .

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

Step 4.2

Multiply $4^{3}$ by $4$ .

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Step 4.2.1

Raise $4$ to the power of $1$ .

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

Step 4.2.2

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

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

Step 4.3

Add $3$ and $1$ .

$4^{4} m^{2} n^{2} (m^{3} n^{3})$

Step 5

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

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Step 5.1

Move $m^{3}$ .

$4^{4} (m^{3} m^{2}) n^{2} n^{3}$

Step 5.2

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

$4^{4} m^{3 + 2} n^{2} n^{3}$

Step 5.3

Add $3$ and $2$ .

$4^{4} m^{5} n^{2} n^{3}$

Step 6

Multiply $n^{2}$ by $n^{3}$ by adding the exponents.

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Step 6.1

Move $n^{3}$ .

$4^{4} m^{5} (n^{3} n^{2})$

Step 6.2

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

$4^{4} m^{5} n^{3 + 2}$

Step 6.3

Add $3$ and $2$ .

$4^{4} m^{5} n^{5}$

Step 7

Raise $4$ to the power of $4$ .

$256 m^{5} n^{5}$