Simplify -8i^88-8i^116-12i^111+8i^14

$- 8 i^{88} - 8 i^{116} - 12 i^{111} + 8 i^{14}$

Step 1

Simplify each term.

Rewrite $i^{88}$ as ${(i^{4})}^{22}$ .

$- 8 {(i^{4})}^{22} - 8 i^{116} - 12 i^{111} + 8 i^{14}$

Rewrite $i^{4}$ as $1$ .

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 8 {({(i^{2})}^{2})}^{22} - 8 i^{116} - 12 i^{111} + 8 i^{14}$

Rewrite $i^{2}$ as $- 1$ .

$- 8 {({(- 1)}^{2})}^{22} - 8 i^{116} - 12 i^{111} + 8 i^{14}$

Raise $- 1$ to the power of $2$ .

$- 8 \cdot 1^{22} - 8 i^{116} - 12 i^{111} + 8 i^{14}$

One to any power is one.

$- 8 \cdot 1 - 8 i^{116} - 12 i^{111} + 8 i^{14}$

Multiply $- 8$ by $1$ .

$- 8 - 8 i^{116} - 12 i^{111} + 8 i^{14}$

Rewrite $i^{116}$ as ${(i^{4})}^{29}$ .

$- 8 - 8 {(i^{4})}^{29} - 12 i^{111} + 8 i^{14}$

Rewrite $i^{4}$ as $1$ .

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 8 - 8 {({(i^{2})}^{2})}^{29} - 12 i^{111} + 8 i^{14}$

Rewrite $i^{2}$ as $- 1$ .

$- 8 - 8 {({(- 1)}^{2})}^{29} - 12 i^{111} + 8 i^{14}$

Raise $- 1$ to the power of $2$ .

$- 8 - 8 \cdot 1^{29} - 12 i^{111} + 8 i^{14}$

One to any power is one.

$- 8 - 8 \cdot 1 - 12 i^{111} + 8 i^{14}$

Multiply $- 8$ by $1$ .

$- 8 - 8 - 12 i^{111} + 8 i^{14}$

Rewrite $i^{111}$ as ${(i^{4})}^{27} (i^{2} \cdot i)$ .

Factor out $i^{108}$ .

$- 8 - 8 - 12 (i^{108} i^{3}) + 8 i^{14}$

Rewrite $i^{108}$ as ${(i^{4})}^{27}$ .

$- 8 - 8 - 12 ({(i^{4})}^{27} i^{3}) + 8 i^{14}$

Factor out $i^{2}$ .

$- 8 - 8 - 12 ({(i^{4})}^{27} (i^{2} \cdot i)) + 8 i^{14}$

Rewrite $i^{4}$ as $1$ .

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 8 - 8 - 12 ({({(i^{2})}^{2})}^{27} (i^{2} \cdot i)) + 8 i^{14}$

Rewrite $i^{2}$ as $- 1$ .

$- 8 - 8 - 12 ({({(- 1)}^{2})}^{27} (i^{2} \cdot i)) + 8 i^{14}$

Raise $- 1$ to the power of $2$ .

$- 8 - 8 - 12 (1^{27} (i^{2} \cdot i)) + 8 i^{14}$

One to any power is one.

$- 8 - 8 - 12 (1 (i^{2} \cdot i)) + 8 i^{14}$

Multiply $i^{2} \cdot i$ by $1$ .

$- 8 - 8 - 12 (i^{2} \cdot i) + 8 i^{14}$

Rewrite $i^{2}$ as $- 1$ .

$- 8 - 8 - 12 (- 1 \cdot i) + 8 i^{14}$

Rewrite $- 1 i$ as $- i$ .

$- 8 - 8 - 12 (- i) + 8 i^{14}$

Multiply $- 1$ by $- 12$ .

$- 8 - 8 + 12 i + 8 i^{14}$

Rewrite $i^{14}$ as ${(i^{4})}^{3} i^{2}$ .

Factor out $i^{12}$ .

$- 8 - 8 + 12 i + 8 (i^{12} i^{2})$

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

$- 8 - 8 + 12 i + 8 ({(i^{4})}^{3} i^{2})$

Rewrite $i^{4}$ as $1$ .

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 8 - 8 + 12 i + 8 ({({(i^{2})}^{2})}^{3} i^{2})$

Rewrite $i^{2}$ as $- 1$ .

$- 8 - 8 + 12 i + 8 ({({(- 1)}^{2})}^{3} i^{2})$

Raise $- 1$ to the power of $2$ .

$- 8 - 8 + 12 i + 8 (1^{3} i^{2})$

One to any power is one.

$- 8 - 8 + 12 i + 8 (1 i^{2})$

Multiply $i^{2}$ by $1$ .

$- 8 - 8 + 12 i + 8 i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$- 8 - 8 + 12 i + 8 \cdot - 1$

Multiply $8$ by $- 1$ .

$- 8 - 8 + 12 i - 8$

Step 2

Simplify by subtracting numbers.

Subtract $8$ from $- 8$ .

$- 16 + 12 i - 8$

Subtract $8$ from $- 16$ .

$- 24 + 12 i$

Simplify -8i^88-8i^116-12i^111+8i^14

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