Basic Math Examples

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

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 $4 m^{2} n$ .

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

Step 1.2

Apply the product rule to $4 m^{2}$ .

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

Step 2

Raise $4$ to the power of $2$ .

$16 {(m^{2})}^{2} n^{2} {(3 m n j)}^{2}$

Step 3

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

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Step 3.1

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

$16 m^{2 \cdot 2} n^{2} {(3 m n j)}^{2}$

Step 3.2

Multiply $2$ by $2$ .

$16 m^{4} n^{2} {(3 m n j)}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $3 m n j$ .

$16 m^{4} n^{2} ({(3 m n)}^{2} j^{2})$

Step 4.2

Apply the product rule to $3 m n$ .

$16 m^{4} n^{2} ({(3 m)}^{2} n^{2} j^{2})$

Step 4.3

Apply the product rule to $3 m$ .

$16 m^{4} n^{2} (3^{2} m^{2} n^{2} j^{2})$

Step 5

Multiply $m^{4}$ by $m^{2}$ by adding the exponents.

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Step 5.1

Move $m^{2}$ .

$16 (m^{2} m^{4}) n^{2} (3^{2} n^{2} j^{2})$

Step 5.2

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

$16 m^{2 + 4} n^{2} (3^{2} n^{2} j^{2})$

Step 5.3

Add $2$ and $4$ .

$16 m^{6} n^{2} (3^{2} n^{2} j^{2})$

Step 6

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

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Step 6.1

Move $n^{2}$ .

$16 m^{6} (n^{2} n^{2}) (3^{2} j^{2})$

Step 6.2

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

$16 m^{6} n^{2 + 2} (3^{2} j^{2})$

Step 6.3

Add $2$ and $2$ .

$16 m^{6} n^{4} (3^{2} j^{2})$

Step 7

Raise $3$ to the power of $2$ .

$16 m^{6} n^{4} (9 j^{2})$

Step 8

Multiply $9$ by $16$ .

$144 m^{6} n^{4} j^{2}$