Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Rewrite using the commutative property of multiplication.

$- 6 {(- 2 \cdot - 1 a^{3} a^{4})}^{2} a^{2}$

Step 3

Multiply $a^{3}$ by $a^{4}$ by adding the exponents.

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Step 3.1

Move $a^{4}$ .

$- 6 {(- 2 \cdot - 1 (a^{4} a^{3}))}^{2} a^{2}$

Step 3.2

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

$- 6 {(- 2 \cdot - 1 a^{4 + 3})}^{2} a^{2}$

Step 3.3

Add $4$ and $3$ .

$- 6 {(- 2 \cdot - 1 a^{7})}^{2} a^{2}$

Step 4

Multiply $- 2$ by $- 1$ .

$- 6 {(2 a^{7})}^{2} a^{2}$

Step 5

Apply the product rule to $2 a^{7}$ .

$- 6 (2^{2} {(a^{7})}^{2}) a^{2}$

Step 6

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

$- 6 (4 {(a^{7})}^{2}) a^{2}$

Step 7

Multiply the exponents in ${(a^{7})}^{2}$ .

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Step 7.1

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

$- 6 (4 a^{7 \cdot 2}) a^{2}$

Step 7.2

Multiply $7$ by $2$ .

$- 6 (4 a^{14}) a^{2}$

Step 8

Multiply $a^{14}$ by $a^{2}$ by adding the exponents.

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Step 8.1

Move $a^{2}$ .

$- 6 (4 (a^{2} a^{14}))$

Step 8.2

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

$- 6 (4 a^{2 + 14})$

Step 8.3

Add $2$ and $14$ .

$- 6 (4 a^{16})$

Step 9

Multiply $4$ by $- 6$ .

$- 24 a^{16}$