Algebra Examples

${(\sqrt{- 10})}^{2}$

Step 1

Rewrite $- 10$ as $- 1 (10)$ .

${\sqrt{- 1 (10)}}^{2}$

Step 2

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

${(\sqrt{- 1} \cdot \sqrt{10})}^{2}$

Step 3

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

${(i \cdot \sqrt{10})}^{2}$

Step 4

Apply the product rule to $i \sqrt{10}$ .

$i^{2} {\sqrt{10}}^{2}$

Step 5

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

$- 1 {\sqrt{10}}^{2}$

Step 6

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$- 1 {(10^{\frac{1}{2}})}^{2}$

Step 6.2

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

$- 1 \cdot 10^{\frac{1}{2} \cdot 2}$

Step 6.3

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

$- 1 \cdot 10^{\frac{2}{2}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$- 1 \cdot 10^{\frac{2}{2}}$

Step 6.4.2

Rewrite the expression.

$- 1 \cdot 10^{1}$

Step 6.5

Evaluate the exponent.

$- 1 \cdot 10$

Step 7

Multiply $- 1$ by $10$ .

$- 10$