Basic Math Examples

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

Step 1

Apply the product rule to $m n^{2}$ .

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

Step 2

Multiply the exponents in ${(n^{2})}^{3}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.2

Multiply $2$ by $3$ .

$m^{3} n^{6} {(m^{2} n^{3})}^{4}$

Step 3

Apply the product rule to $m^{2} n^{3}$ .

$m^{3} n^{6} ({(m^{2})}^{4} {(n^{3})}^{4})$

Step 4

Multiply the exponents in ${(m^{2})}^{4}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$m^{3} n^{6} (m^{2 \cdot 4} {(n^{3})}^{4})$

Step 4.2

Multiply $2$ by $4$ .

$m^{3} n^{6} (m^{8} {(n^{3})}^{4})$

Step 5

Multiply $m^{3}$ by $m^{8}$ by adding the exponents.

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Step 5.1

Move $m^{8}$ .

$m^{8} m^{3} n^{6} {(n^{3})}^{4}$

Step 5.2

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

$m^{8 + 3} n^{6} {(n^{3})}^{4}$

Step 5.3

Add $8$ and $3$ .

$m^{11} n^{6} {(n^{3})}^{4}$

Step 6

Multiply the exponents in ${(n^{3})}^{4}$ .

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Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$m^{11} n^{6} n^{3 \cdot 4}$

Step 6.2

Multiply $3$ by $4$ .

$m^{11} n^{6} n^{12}$

Step 7

Multiply $n^{6}$ by $n^{12}$ by adding the exponents.

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Step 7.1

Move $n^{12}$ .

$m^{11} (n^{12} n^{6})$

Step 7.2

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

$m^{11} n^{12 + 6}$

Step 7.3

Add $12$ and $6$ .

$m^{11} n^{18}$