Basic Math Examples

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

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

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

$3 m n^{2}$ .

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

Step 1.2

Apply the product rule to

$3 m$ .

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

Step 2

Raise

$3$ to the power of

$3$ .

$27 m^{3} {(n^{2})}^{3} \cdot {(3 m^{3} n)}^{3}$

Step 3

Multiply the exponents in

${(n^{2})}^{3}$ .

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Step 3.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$27 m^{3} n^{2 \cdot 3} \cdot {(3 m^{3} n)}^{3}$

Step 3.2

Multiply

$2$ by

$3$ .

$27 m^{3} n^{6} \cdot {(3 m^{3} n)}^{3}$

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

$3 m^{3} n$ .

$27 m^{3} n^{6} \cdot ({(3 m^{3})}^{3} n^{3})$

Step 4.2

Apply the product rule to

$3 m^{3}$ .

$27 m^{3} n^{6} \cdot (3^{3} {(m^{3})}^{3} n^{3})$

Step 5

Multiply

$n^{6}$ by

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

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Step 5.1

Move

$n^{3}$ .

$27 m^{3} (n^{3} n^{6}) \cdot (3^{3} {(m^{3})}^{3})$

Step 5.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$27 m^{3} n^{3 + 6} \cdot (3^{3} {(m^{3})}^{3})$

Step 5.3

Add

$3$ and

$6$ .

$27 m^{3} n^{9} \cdot (3^{3} {(m^{3})}^{3})$

Step 6

Raise

$3$ to the power of

$3$ .

$27 m^{3} n^{9} \cdot (27 {(m^{3})}^{3})$

Step 7

Multiply the exponents in

${(m^{3})}^{3}$ .

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Step 7.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$27 m^{3} n^{9} \cdot (27 m^{3 \cdot 3})$

Step 7.2

Multiply

$3$ by

$3$ .

$27 m^{3} n^{9} \cdot (27 m^{9})$

Step 8

Multiply

$m^{3}$ by

$m^{9}$ by adding the exponents.

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Step 8.1

Move

$m^{9}$ .

$27 (m^{9} m^{3}) n^{9} \cdot 27$

Step 8.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$27 m^{9 + 3} n^{9} \cdot 27$

Step 8.3

Add

$9$ and

$3$ .

$27 m^{12} n^{9} \cdot 27$

Step 9

Multiply

$27$ by

$27$ .

$729 m^{12} n^{9}$