Finite Math Examples

27^{- \frac{2}{3}}

$27^{- \frac{2}{3}}$

Step 1

Convert the radian measure to degrees.

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Step 1.1

To convert radians to degrees, multiply by

\frac{180}{π}

$\frac{180}{π}$ , since a full circle is

360 °

$360 °$ or

2 π

$2 π$ radians.

(27^{- \frac{2}{3}}) \cdot \frac{180 °}{π}

$(27^{- \frac{2}{3}}) \cdot \frac{180 °}{π}$

Step 1.2

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{27^{\frac{2}{3}}} \cdot \frac{180}{π}

$\frac{1}{27^{\frac{2}{3}}} \cdot \frac{180}{π}$

Step 1.3

Combine fractions.

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Step 1.3.1

Combine.

\frac{1 \cdot 180}{27^{\frac{2}{3}} π}

$\frac{1 \cdot 180}{27^{\frac{2}{3}} π}$

Step 1.3.2

Multiply

180

$180$ by

1

$1$ .

\frac{180}{27^{\frac{2}{3}} π}

$\frac{180}{27^{\frac{2}{3}} π}$

\frac{180}{27^{\frac{2}{3}} π}

$\frac{180}{27^{\frac{2}{3}} π}$

Step 1.4

Simplify the denominator.

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Step 1.4.1

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

\frac{180}{{(3^{3})}^{\frac{2}{3}} π}

$\frac{180}{{(3^{3})}^{\frac{2}{3}} π}$

Step 1.4.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{180}{3^{3 (\frac{2}{3})} π}$

Step 1.4.3

Cancel the common factor of

$3$ .

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Step 1.4.3.1

Cancel the common factor.

$\frac{180}{3^{3 (\frac{2}{3})} π}$

Step 1.4.3.2

Rewrite the expression.

$\frac{180}{3^{2} π}$

$\frac{180}{3^{2} π}$

Step 1.4.4

Raise

$3$ to the power of

$2$ .

$\frac{180}{9 π}$

$\frac{180}{9 π}$

Step 1.5

Cancel the common factor of

$180$ and

$9$ .

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Step 1.5.1

Factor

$9$ out of

$180$ .

$\frac{9 \cdot 20}{9 π}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor

$9$ out of

$9 π$ .

$\frac{9 \cdot 20}{9 (π)}$

Step 1.5.2.2

Cancel the common factor.

$\frac{9 \cdot 20}{9 π}$

Step 1.5.2.3

Rewrite the expression.

$\frac{20}{π}$

$\frac{20}{π}$

$\frac{20}{π}$

Step 1.6

$π$ is approximately equal to

$3.14159265$ .

$\frac{20}{3.14159265}$

Step 1.7

Convert to a decimal.

$6.36619772 °$

$6.36619772 °$

Step 2

The angle is in the first quadrant.

Quadrant

$1$

Step 3

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$