Basic Math Examples

$- a^{3} \cdot (2 a^{2}) \cdot (- 5 a) \cdot (3 a^{4})$

Step 1

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

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Step 1.1

Move $a^{2}$ .

$- (a^{2} a^{3}) \cdot 2 \cdot (- 5 a) \cdot (3 a^{4})$

Step 1.2

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

$- a^{2 + 3} \cdot 2 \cdot (- 5 a) \cdot (3 a^{4})$

Step 1.3

Add $2$ and $3$ .

$- a^{5} \cdot 2 \cdot (- 5 a) \cdot (3 a^{4})$

Step 2

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

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Step 2.1

Move $a$ .

$- (a \cdot a^{5}) \cdot 2 \cdot - 5 \cdot (3 a^{4})$

Step 2.2

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

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Step 2.2.1

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

$- (a^{1} a^{5}) \cdot 2 \cdot - 5 \cdot (3 a^{4})$

Step 2.2.2

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

$- a^{1 + 5} \cdot 2 \cdot - 5 \cdot (3 a^{4})$

Step 2.3

Add $1$ and $5$ .

$- a^{6} \cdot 2 \cdot - 5 \cdot (3 a^{4})$

Step 3

Multiply $a^{6}$ by $a^{4}$ by adding the exponents.

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Step 3.1

Move $a^{4}$ .

$- (a^{4} a^{6}) \cdot 2 \cdot - 5 \cdot 3$

Step 3.2

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

$- a^{4 + 6} \cdot 2 \cdot - 5 \cdot 3$

Step 3.3

Add $4$ and $6$ .

$- a^{10} \cdot 2 \cdot - 5 \cdot 3$

Step 4

Multiply $2$ by $- 1$ .

$- 2 a^{10} \cdot - 5 \cdot 3$

Step 5

Multiply $- 5$ by $- 2$ .

$10 a^{10} \cdot 3$

Step 6

Multiply $3$ by $10$ .

$30 a^{10}$