Basic Math Examples

${(3 k^{2} \cdot k^{2} \cdot (2 k))}^{3}$

Step 1

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

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Step 1.1

Move $k^{2}$ .

${(3 (k^{2} k^{2}) \cdot (2 k))}^{3}$

Step 1.2

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

${(3 k^{2 + 2} \cdot (2 k))}^{3}$

Step 1.3

Add $2$ and $2$ .

${(3 k^{4} \cdot (2 k))}^{3}$

Step 2

Rewrite using the commutative property of multiplication.

${(3 \cdot 2 k^{4} k)}^{3}$

Step 3

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

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Step 3.1

Move $k$ .

${(3 \cdot 2 (k \cdot k^{4}))}^{3}$

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

${(3 \cdot 2 k^{1 + 4})}^{3}$

Step 3.3

Add $1$ and $4$ .

${(3 \cdot 2 k^{5})}^{3}$

Step 4

Multiply $3$ by $2$ .

${(6 k^{5})}^{3}$

Step 5

Apply the product rule to $6 k^{5}$ .

$6^{3} {(k^{5})}^{3}$

Step 6

Raise $6$ to the power of $3$ .

$216 {(k^{5})}^{3}$

Step 7

Multiply the exponents in ${(k^{5})}^{3}$ .

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Step 7.1

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

$216 k^{5 \cdot 3}$

Step 7.2

Multiply $5$ by $3$ .

$216 k^{15}$