Trigonometry Examples

$\frac{- 8}{\sqrt{4.123} \cdot \sqrt{4.123}}$

Step 1

Simplify the denominator.

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Step 1.1

Raise $\sqrt{4.123}$ to the power of $1$ .

$\frac{- 8}{{\sqrt{4.123}}^{1} \sqrt{4.123}}$

Step 1.2

Raise $\sqrt{4.123}$ to the power of $1$ .

$\frac{- 8}{{\sqrt{4.123}}^{1} {\sqrt{4.123}}^{1}}$

Step 1.3

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

$\frac{- 8}{{\sqrt{4.123}}^{1 + 1}}$

Step 1.4

Add $1$ and $1$ .

$\frac{- 8}{{\sqrt{4.123}}^{2}}$

Step 2

Simplify by cancelling exponent with radical.

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Step 2.1

Rewrite ${\sqrt{4.123}}^{2}$ as $4.123$ .

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Step 2.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4.123}$ as ${4.123}^{\frac{1}{2}}$ .

$\frac{- 8}{{({4.123}^{\frac{1}{2}})}^{2}}$

Step 2.1.2

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

$\frac{- 8}{{4.123}^{\frac{1}{2} \cdot 2}}$

Step 2.1.3

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

$\frac{- 8}{{4.123}^{\frac{2}{2}}}$

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Cancel the common factor.

$\frac{- 8}{{4.123}^{\frac{2}{2}}}$

Step 2.1.4.2

Rewrite the expression.

$\frac{- 8}{{4.123}^{1}}$

Step 2.1.5

Evaluate the exponent.

$\frac{- 8}{4.123}$

Step 2.2

Divide $- 8$ by $4.123$ .

$- 1.9403347$