Trigonometry Examples

$\frac{50 \sqrt{2} (- \sqrt{2})}{2}$

Step 1

Cancel the common factor of $50$ and $2$ .

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Step 1.1

Factor $2$ out of $50 \sqrt{2} (- \sqrt{2})$ .

$\frac{2 (25 \sqrt{2} (- \sqrt{2}))}{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

$\frac{2 (25 \sqrt{2} (- \sqrt{2}))}{2 (1)}$

Step 1.2.2

Cancel the common factor.

$\frac{2 (25 \sqrt{2} (- \sqrt{2}))}{2 \cdot 1}$

Step 1.2.3

Rewrite the expression.

$\frac{25 \sqrt{2} (- \sqrt{2})}{1}$

Step 1.2.4

Divide $25 \sqrt{2} (- \sqrt{2})$ by $1$ .

$25 \sqrt{2} (- \sqrt{2})$

Step 2

Multiply $25 \sqrt{2} (- \sqrt{2})$ .

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Step 2.1

Multiply $- 1$ by $25$ .

$- 25 \sqrt{2} \sqrt{2}$

Step 2.2

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

$- 25 ({\sqrt{2}}^{1} \sqrt{2})$

Step 2.3

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

$- 25 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 2.4

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

$- 25 {\sqrt{2}}^{1 + 1}$

Step 2.5

Add $1$ and $1$ .

$- 25 {\sqrt{2}}^{2}$

Step 3

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

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Step 3.1

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

$- 25 {(2^{\frac{1}{2}})}^{2}$

Step 3.2

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

$- 25 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 3.3

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

$- 25 \cdot 2^{\frac{2}{2}}$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

$- 25 \cdot 2^{\frac{2}{2}}$

Step 3.4.2

Rewrite the expression.

$- 25 \cdot 2^{1}$

Step 3.5

Evaluate the exponent.

$- 25 \cdot 2$

Step 4

Multiply $- 25$ by $2$ .

$- 50$