Trigonometry Examples

${(\frac{8}{\sqrt{353}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{8}{\sqrt{353}}$ by $\frac{\sqrt{353}}{\sqrt{353}}$ .

${(\frac{8}{\sqrt{353}} \cdot \frac{\sqrt{353}}{\sqrt{353}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{8}{\sqrt{353}}$ by $\frac{\sqrt{353}}{\sqrt{353}}$ .

${(\frac{8 \sqrt{353}}{\sqrt{353} \sqrt{353}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.2

Raise $\sqrt{353}$ to the power of $1$ .

${(\frac{8 \sqrt{353}}{{\sqrt{353}}^{1} \sqrt{353}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.3

Raise $\sqrt{353}$ to the power of $1$ .

${(\frac{8 \sqrt{353}}{{\sqrt{353}}^{1} {\sqrt{353}}^{1}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.4

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

${(\frac{8 \sqrt{353}}{{\sqrt{353}}^{1 + 1}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.5

Add $1$ and $1$ .

${(\frac{8 \sqrt{353}}{{\sqrt{353}}^{2}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.6

Rewrite ${\sqrt{353}}^{2}$ as $353$ .

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Step 1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{353}$ as $353^{\frac{1}{2}}$ .

${(\frac{8 \sqrt{353}}{{(353^{\frac{1}{2}})}^{2}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.6.2

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

${(\frac{8 \sqrt{353}}{353^{\frac{1}{2} \cdot 2}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.6.3

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

${(\frac{8 \sqrt{353}}{353^{\frac{2}{2}}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.6.4

Cancel the common factor of $2$ .

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Step 1.2.6.4.1

Cancel the common factor.

${(\frac{8 \sqrt{353}}{353^{\frac{2}{2}}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.6.4.2

Rewrite the expression.

${(\frac{8 \sqrt{353}}{353^{1}})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.2.6.5

Evaluate the exponent.

${(\frac{8 \sqrt{353}}{353})}^{2} - (- \frac{17}{\sqrt{353}})$

Step 1.3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.3.1

Apply the product rule to $\frac{8 \sqrt{353}}{353}$ .

$\frac{{(8 \sqrt{353})}^{2}}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.3.2

Apply the product rule to $8 \sqrt{353}$ .

$\frac{8^{2} {\sqrt{353}}^{2}}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Raise $8$ to the power of $2$ .

$\frac{64 {\sqrt{353}}^{2}}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.4.2

Rewrite ${\sqrt{353}}^{2}$ as $353$ .

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Step 1.4.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{353}$ as $353^{\frac{1}{2}}$ .

$\frac{64 {(353^{\frac{1}{2}})}^{2}}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.4.2.2

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

$\frac{64 \cdot 353^{\frac{1}{2} \cdot 2}}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.4.2.3

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

$\frac{64 \cdot 353^{\frac{2}{2}}}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.4.2.4

Cancel the common factor of $2$ .

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Step 1.4.2.4.1

Cancel the common factor.

$\frac{64 \cdot 353^{\frac{2}{2}}}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.4.2.4.2

Rewrite the expression.

$\frac{64 \cdot 353^{1}}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.4.2.5

Evaluate the exponent.

$\frac{64 \cdot 353}{353^{2}} - (- \frac{17}{\sqrt{353}})$

Step 1.5

Raise $353$ to the power of $2$ .

$\frac{64 \cdot 353}{124609} - (- \frac{17}{\sqrt{353}})$

Step 1.6

Multiply $64$ by $353$ .

$\frac{22592}{124609} - (- \frac{17}{\sqrt{353}})$

Step 1.7

Cancel the common factor of $22592$ and $124609$ .

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Step 1.7.1

Factor $353$ out of $22592$ .

$\frac{353 (64)}{124609} - (- \frac{17}{\sqrt{353}})$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $353$ out of $124609$ .

$\frac{353 \cdot 64}{353 \cdot 353} - (- \frac{17}{\sqrt{353}})$

Step 1.7.2.2

Cancel the common factor.

$\frac{353 \cdot 64}{353 \cdot 353} - (- \frac{17}{\sqrt{353}})$

Step 1.7.2.3

Rewrite the expression.

$\frac{64}{353} - (- \frac{17}{\sqrt{353}})$

Step 1.8

Multiply $\frac{17}{\sqrt{353}}$ by $\frac{\sqrt{353}}{\sqrt{353}}$ .

$\frac{64}{353} - - (\frac{17}{\sqrt{353}} \cdot \frac{\sqrt{353}}{\sqrt{353}})$

Step 1.9

Combine and simplify the denominator.

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Step 1.9.1

Multiply $\frac{17}{\sqrt{353}}$ by $\frac{\sqrt{353}}{\sqrt{353}}$ .

$\frac{64}{353} - - \frac{17 \sqrt{353}}{\sqrt{353} \sqrt{353}}$

Step 1.9.2

Raise $\sqrt{353}$ to the power of $1$ .

$\frac{64}{353} - - \frac{17 \sqrt{353}}{{\sqrt{353}}^{1} \sqrt{353}}$

Step 1.9.3

Raise $\sqrt{353}$ to the power of $1$ .

$\frac{64}{353} - - \frac{17 \sqrt{353}}{{\sqrt{353}}^{1} {\sqrt{353}}^{1}}$

Step 1.9.4

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

$\frac{64}{353} - - \frac{17 \sqrt{353}}{{\sqrt{353}}^{1 + 1}}$

Step 1.9.5

Add $1$ and $1$ .

$\frac{64}{353} - - \frac{17 \sqrt{353}}{{\sqrt{353}}^{2}}$

Step 1.9.6

Rewrite ${\sqrt{353}}^{2}$ as $353$ .

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Step 1.9.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{353}$ as $353^{\frac{1}{2}}$ .

$\frac{64}{353} - - \frac{17 \sqrt{353}}{{(353^{\frac{1}{2}})}^{2}}$

Step 1.9.6.2

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

$\frac{64}{353} - - \frac{17 \sqrt{353}}{353^{\frac{1}{2} \cdot 2}}$

Step 1.9.6.3

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

$\frac{64}{353} - - \frac{17 \sqrt{353}}{353^{\frac{2}{2}}}$

Step 1.9.6.4

Cancel the common factor of $2$ .

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Step 1.9.6.4.1

Cancel the common factor.

$\frac{64}{353} - - \frac{17 \sqrt{353}}{353^{\frac{2}{2}}}$

Step 1.9.6.4.2

Rewrite the expression.

$\frac{64}{353} - - \frac{17 \sqrt{353}}{353^{1}}$

Step 1.9.6.5

Evaluate the exponent.

$\frac{64}{353} - - \frac{17 \sqrt{353}}{353}$

Step 1.10

Multiply $- - \frac{17 \sqrt{353}}{353}$ .

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Step 1.10.1

Multiply $- 1$ by $- 1$ .

$\frac{64}{353} + 1 \frac{17 \sqrt{353}}{353}$

Step 1.10.2

Multiply $\frac{17 \sqrt{353}}{353}$ by $1$ .

$\frac{64}{353} + \frac{17 \sqrt{353}}{353}$

Step 2

Combine the numerators over the common denominator.

$\frac{64 + 17 \sqrt{353}}{353}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{64 + 17 \sqrt{353}}{353}$

Decimal Form:

$1.08612181 \dots$