Trigonometry Examples

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

Step 1

Multiply $- 1$ by $- 1$ by adding the exponents.

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Step 1.1

Move $- 1$ .

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

Step 1.2

Multiply $- 1$ by $- 1$ .

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

Step 2

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

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

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $- 1 (1)$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 4

Multiply $1^{2}$ by $1^{2}$ by adding the exponents.

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Step 4.1

Move $1^{2}$ .

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

Step 4.2

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

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

Step 4.3

Add $2$ and $2$ .

$\sqrt{1^{4} \cdot 2^{2}}$

Step 5

One to any power is one.

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

Step 6

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

$\sqrt{1 \cdot 4}$

Step 7

Multiply $4$ by $1$ .

$\sqrt{4}$

Step 8

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2}}$

Step 9

Pull terms out from under the radical, assuming positive real numbers.

$2$