Basic Math Examples

$(- 5 a) (2 a^{3}) (- 4 a^{7})$

Step 1

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

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Step 1.1

Move $a^{3}$ .

$- 5 (a^{3} a) \cdot 2 (- 4 a^{7})$

Step 1.2

Multiply $a^{3}$ by $a$ .

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Step 1.2.1

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

$- 5 (a^{3} a^{1}) \cdot 2 (- 4 a^{7})$

Step 1.2.2

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

$- 5 a^{3 + 1} \cdot 2 (- 4 a^{7})$

Step 1.3

Add $3$ and $1$ .

$- 5 a^{4} \cdot 2 (- 4 a^{7})$

Step 2

Multiply $a^{4}$ by $a^{7}$ by adding the exponents.

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Step 2.1

Move $a^{7}$ .

$- 5 (a^{7} a^{4}) \cdot 2 \cdot - 4$

Step 2.2

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

$- 5 a^{7 + 4} \cdot 2 \cdot - 4$

Step 2.3

Add $7$ and $4$ .

$- 5 a^{11} \cdot 2 \cdot - 4$

Step 3

Multiply $2$ by $- 5$ .

$- 10 a^{11} \cdot - 4$

Step 4

Multiply $- 4$ by $- 10$ .

$40 a^{11}$