Algebra Examples

$(- i \sqrt{2}) (i \sqrt{2})$

Step 1

Multiply $(- i \sqrt{2}) (i \sqrt{2})$ .

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Step 1.1

Raise $i$ to the power of $1$ .

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

Step 1.2

Raise $i$ to the power of $1$ .

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

Step 1.3

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

$- i^{1 + 1} \sqrt{2} \sqrt{2}$

Step 1.4

Add $1$ and $1$ .

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

Step 1.5

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 1.6

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 1.7

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

$- i^{2} {\sqrt{2}}^{1 + 1}$

Step 1.8

Add $1$ and $1$ .

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

Step 2

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

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

Step 3

Multiply.

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Step 3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.2

Multiply ${\sqrt{2}}^{2}$ by $1$ .

${\sqrt{2}}^{2}$

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

$2^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$2^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

$2^{1}$

Step 4.5

Evaluate the exponent.

$2$