Basic Math Examples

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

Step 1

Multiply $a^{2}$ by $a^{5}$ by adding the exponents.

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Step 1.1

Move $a^{5}$ .

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

Step 1.2

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

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

Step 1.3

Add $5$ and $2$ .

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

Multiply $3$ by $- 1$ .

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

Step 4

Apply the product rule to $2 a^{3}$ .

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

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

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

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

Step 7

Multiply $- 3$ by $4$ .

$- 12 a^{7} {(a^{3})}^{2} \cdot - 4$

Step 8

Multiply the exponents in ${(a^{3})}^{2}$ .

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Step 8.1

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

$- 12 a^{7} a^{3 \cdot 2} \cdot - 4$

Step 8.2

Multiply $3$ by $2$ .

$- 12 a^{7} a^{6} \cdot - 4$

Step 9

Multiply $a^{7}$ by $a^{6}$ by adding the exponents.

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Step 9.1

Move $a^{6}$ .

$- 12 (a^{6} a^{7}) \cdot - 4$

Step 9.2

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

$- 12 a^{6 + 7} \cdot - 4$

Step 9.3

Add $6$ and $7$ .

$- 12 a^{13} \cdot - 4$

Step 10

Multiply $- 4$ by $- 12$ .

$48 a^{13}$