Simplify (i square root of 7)^2*2i

${(i \sqrt{7})}^{2} \cdot 2 i$

Step 1

Apply the product rule to $i \sqrt{7}$ .

$i^{2} {\sqrt{7}}^{2} \cdot (2 i)$

Step 2

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

$- 1 {\sqrt{7}}^{2} \cdot (2 i)$

Step 3

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$- 1 {(7^{\frac{1}{2}})}^{2} \cdot (2 i)$

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

$- 1 \cdot 7^{\frac{1}{2} \cdot 2} \cdot (2 i)$

Combine $\frac{1}{2}$ and $2$ .

$- 1 \cdot 7^{\frac{2}{2}} \cdot (2 i)$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 1 \cdot 7^{\frac{2}{2}} \cdot (2 i)$

Rewrite the expression.

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

Evaluate the exponent.

$- 1 \cdot 7 \cdot (2 i)$

Step 4

Multiply.

Multiply $- 1$ by $7$ .

$- 7 \cdot (2 i)$

Multiply $2$ by $- 7$ .

$- 14 i$