Finite Math Examples

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

Step 1

Convert the radian measure to degrees.

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Step 1.1

To convert radians to degrees, multiply by $\frac{180}{π}$ , since a full circle is $360 °$ or $2 π$ radians.

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

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 1.3

Combine fractions.

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Step 1.3.1

Combine.

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

Step 1.3.2

Multiply $180$ by $1$ .

$\frac{180}{27^{\frac{2}{3}} π}$

Step 1.4

Simplify the denominator.

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Step 1.4.1

Rewrite $27$ as $3^{3}$ .

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

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.

$\frac{180}{3^{2} π}$

Step 1.4.4

Raise $3$ to the power of $2$ .

$\frac{180}{9 π}$

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.

$\frac{20}{π}$

Step 1.6

$π$ is approximately equal to $3.14159265$ .

$\frac{20}{3.14159265}$

Step 1.7

Convert to a decimal.

$6.36619772 °$

Step 2

The angle is in the first quadrant.

Quadrant $1$

Step 3