Basic Math Examples

$2 q^{0} (q^{2}) {(3 q)}^{3}$

Step 1

Multiply $q^{0}$ by $q^{2}$ by adding the exponents.

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Step 1.1

Move $q^{2}$ .

$2 (q^{2} q^{0}) {(3 q)}^{3}$

Step 1.2

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

$2 q^{2 + 0} {(3 q)}^{3}$

Step 1.3

Add $2$ and $0$ .

$2 q^{2} {(3 q)}^{3}$

Step 2

Apply the product rule to $3 q$ .

$2 q^{2} (3^{3} q^{3})$

Step 3

Rewrite using the commutative property of multiplication.

$2 \cdot 3^{3} q^{2} q^{3}$

Step 4

Multiply $q^{2}$ by $q^{3}$ by adding the exponents.

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Step 4.1

Move $q^{3}$ .

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

Step 4.2

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

$2 \cdot 3^{3} q^{3 + 2}$

Step 4.3

Add $3$ and $2$ .

$2 \cdot 3^{3} q^{5}$

Step 5

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

$2 \cdot 27 q^{5}$

Step 6

Multiply $2$ by $27$ .

$54 q^{5}$