Algebra Examples

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

Step 1

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

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

Step 2

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

$8 {(m^{2})}^{3} \cdot {(3 m^{3})}^{2}$

Step 3

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

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Step 3.1

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

$8 m^{2 \cdot 3} \cdot {(3 m^{3})}^{2}$

Step 3.2

Multiply $2$ by $3$ .

$8 m^{6} \cdot {(3 m^{3})}^{2}$

Step 4

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

$8 m^{6} \cdot (3^{2} {(m^{3})}^{2})$

Step 5

Rewrite using the commutative property of multiplication.

$8 \cdot 3^{2} m^{6} {(m^{3})}^{2}$

Step 6

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

$8 \cdot 9 m^{6} {(m^{3})}^{2}$

Step 7

Multiply $8$ by $9$ .

$72 m^{6} {(m^{3})}^{2}$

Step 8

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

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Step 8.1

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

$72 m^{6} m^{3 \cdot 2}$

Step 8.2

Multiply $3$ by $2$ .

$72 m^{6} m^{6}$

Step 9

Multiply $m^{6}$ by $m^{6}$ by adding the exponents.

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Step 9.1

Move $m^{6}$ .

$72 (m^{6} m^{6})$

Step 9.2

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

$72 m^{6 + 6}$

Step 9.3

Add $6$ and $6$ .

$72 m^{12}$