Algebra Examples

$17 {(a^{2 n + 1})}^{4} \cdot 2 a^{7 n - 12}$

Step 1

Rewrite using the commutative property of multiplication.

$17 \cdot 2 {(a^{2 n + 1})}^{4} a^{7 n - 12}$

Step 2

Multiply $17$ by $2$ .

$34 {(a^{2 n + 1})}^{4} a^{7 n - 12}$

Step 3

Multiply the exponents in ${(a^{2 n + 1})}^{4}$ .

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Step 3.1

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

$34 a^{(2 n + 1) \cdot 4} a^{7 n - 12}$

Step 3.2

Apply the distributive property.

$34 a^{2 n \cdot 4 + 1 \cdot 4} a^{7 n - 12}$

Step 3.3

Multiply $4$ by $2$ .

$34 a^{8 n + 1 \cdot 4} a^{7 n - 12}$

Step 3.4

Multiply $4$ by $1$ .

$34 a^{8 n + 4} a^{7 n - 12}$

Step 4

Multiply $a^{8 n + 4}$ by $a^{7 n - 12}$ by adding the exponents.

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Step 4.1

Move $a^{7 n - 12}$ .

$34 (a^{7 n - 12} a^{8 n + 4})$

Step 4.2

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

$34 a^{7 n - 12 + 8 n + 4}$

Step 4.3

Add $7 n$ and $8 n$ .

$34 a^{15 n - 12 + 4}$

Step 4.4

Add $- 12$ and $4$ .

$34 a^{15 n - 8}$