Simplify 1/45 square root of -8^4+2(86)^2+2(82)^2-6^4+2(612)^2-12^4

$\frac{1}{4} \cdot 5 \cdot \sqrt{- 8^{4} + 2} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Step 1

Simplify each term.

Combine $\frac{1}{4}$ and $5$ .

$\frac{5}{4} \cdot \sqrt{- 8^{4} + 2} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Raise $8$ to the power of $4$ .

$\frac{5}{4} \cdot \sqrt{- 1 \cdot 4096 + 2} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Multiply $- 1$ by $4096$ .

$\frac{5}{4} \cdot \sqrt{- 4096 + 2} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Add $- 4096$ and $2$ .

$\frac{5}{4} \cdot \sqrt{- 4094} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Rewrite $- 4094$ as $- 1 (4094)$ .

$\frac{5}{4} \cdot \sqrt{- 1 (4094)} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Rewrite $\sqrt{- 1 (4094)}$ as $\sqrt{- 1} \cdot \sqrt{4094}$ .

$\frac{5}{4} \cdot (\sqrt{- 1} \cdot \sqrt{4094}) \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{5}{4} \cdot (i \cdot \sqrt{4094}) \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Multiply $\frac{5}{4} (i \sqrt{4094})$ .

Combine $i$ and $\frac{5}{4}$ .

$\frac{i \cdot 5}{4} \sqrt{4094} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Combine $\frac{i \cdot 5}{4}$ and $\sqrt{4094}$ .

$\frac{i \cdot 5 \sqrt{4094}}{4} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Move $5$ to the left of $i$ .

$\frac{5 i \sqrt{4094}}{4} \cdot {(8 \cdot 6)}^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Multiply $8$ by $6$ .

$\frac{5 i \sqrt{4094}}{4} \cdot 48^{2} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Raise $48$ to the power of $2$ .

$\frac{5 i \sqrt{4094}}{4} \cdot 2304 + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Cancel the common factor of $4$ .

Factor $4$ out of $2304$ .

$\frac{5 i \sqrt{4094}}{4} \cdot (4 (576)) + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Cancel the common factor.

$\frac{5 i \sqrt{4094}}{4} \cdot (4 \cdot 576) + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Rewrite the expression.

$5 i \sqrt{4094} \cdot 576 + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Multiply $576$ by $5$ .

$2880 i \sqrt{4094} + 2 \cdot {(8 \cdot 2)}^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Multiply $8$ by $2$ .

$2880 i \sqrt{4094} + 2 \cdot 16^{2} - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Raise $16$ to the power of $2$ .

$2880 i \sqrt{4094} + 2 \cdot 256 - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Multiply $2$ by $256$ .

$2880 i \sqrt{4094} + 512 - 6^{4} + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Raise $6$ to the power of $4$ .

$2880 i \sqrt{4094} + 512 - 1 \cdot 1296 + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Multiply $- 1$ by $1296$ .

$2880 i \sqrt{4094} + 512 - 1296 + 2 \cdot {(6 \cdot 12)}^{2} - 12^{4}$

Multiply $6$ by $12$ .

$2880 i \sqrt{4094} + 512 - 1296 + 2 \cdot 72^{2} - 12^{4}$

Raise $72$ to the power of $2$ .

$2880 i \sqrt{4094} + 512 - 1296 + 2 \cdot 5184 - 12^{4}$

Multiply $2$ by $5184$ .

$2880 i \sqrt{4094} + 512 - 1296 + 10368 - 12^{4}$

Raise $12$ to the power of $4$ .

$2880 i \sqrt{4094} + 512 - 1296 + 10368 - 1 \cdot 20736$

Multiply $- 1$ by $20736$ .

$2880 i \sqrt{4094} + 512 - 1296 + 10368 - 20736$

Step 2

Simplify the expression.

Subtract $1296$ from $512$ .

$2880 i \sqrt{4094} - 784 + 10368 - 20736$

Add $- 784$ and $10368$ .

$2880 i \sqrt{4094} + 9584 - 20736$

Subtract $20736$ from $9584$ .

$2880 i \sqrt{4094} - 11152$

Reorder $2880 i \sqrt{4094}$ and $- 11152$ .

$- 11152 + 2880 i \sqrt{4094}$

Simplify 1/4*5* square root of -8^4+2*(8*6)^2+2*(8*2)^2-6^4+2*(6*12)^2-12^4

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Simplify 1/45 square root of -8^4+2(86)^2+2(82)^2-6^4+2(612)^2-12^4