Basic Math Examples

${(- 2 m)}^{2} {(3 m^{8})}^{2}$

Step 1

Apply the product rule to $- 2 m$ .

${(- 2)}^{2} m^{2} {(3 m^{8})}^{2}$

Step 2

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

$4 m^{2} {(3 m^{8})}^{2}$

Step 3

Apply the product rule to $3 m^{8}$ .

$4 m^{2} (3^{2} {(m^{8})}^{2})$

Step 4

Rewrite using the commutative property of multiplication.

$4 \cdot 3^{2} m^{2} {(m^{8})}^{2}$

Step 5

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

$4 \cdot 9 m^{2} {(m^{8})}^{2}$

Step 6

Multiply $4$ by $9$ .

$36 m^{2} {(m^{8})}^{2}$

Step 7

Multiply the exponents in ${(m^{8})}^{2}$ .

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Step 7.1

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

$36 m^{2} m^{8 \cdot 2}$

Step 7.2

Multiply $8$ by $2$ .

$36 m^{2} m^{16}$

Step 8

Multiply $m^{2}$ by $m^{16}$ by adding the exponents.

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Step 8.1

Move $m^{16}$ .

$36 (m^{16} m^{2})$

Step 8.2

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

$36 m^{16 + 2}$

Step 8.3

Add $16$ and $2$ .

$36 m^{18}$