Basic Math Examples

$a^{5} \cdot (3 b^{9}) \cdot (6 a b)$

Step 1

Multiply $a^{5}$ by $a$ by adding the exponents.

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Step 1.1

Move $a$ .

$a \cdot a^{5} \cdot (3 b^{9}) \cdot (6 b)$

Step 1.2

Multiply $a$ by $a^{5}$ .

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Step 1.2.1

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

$a^{1} a^{5} \cdot (3 b^{9}) \cdot (6 b)$

Step 1.2.2

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

$a^{1 + 5} \cdot (3 b^{9}) \cdot (6 b)$

Step 1.3

Add $1$ and $5$ .

$a^{6} \cdot (3 b^{9}) \cdot (6 b)$

Step 2

Multiply $b^{9}$ by $b$ by adding the exponents.

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Step 2.1

Move $b$ .

$a^{6} \cdot (3 (b \cdot b^{9})) \cdot 6$

Step 2.2

Multiply $b$ by $b^{9}$ .

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Step 2.2.1

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

$a^{6} \cdot (3 (b^{1} b^{9})) \cdot 6$

Step 2.2.2

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

$a^{6} \cdot (3 b^{1 + 9}) \cdot 6$

Step 2.3

Add $1$ and $9$ .

$a^{6} \cdot (3 b^{10}) \cdot 6$

Step 3

Rewrite using the commutative property of multiplication.

$3 a^{6} b^{10} \cdot 6$

Step 4

Multiply $6$ by $3$ .

$18 a^{6} b^{10}$