1Cademy - Example of Simplifying $$\frac{(\frac{1}{3})^2}{2^3+2}$$

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Simplifying Complex Fractions

Example

Example of Simplifying $\frac{(\frac{1}{3})^2}{2^3+2}$

To simplify the complex fraction $\frac{(\frac{1}{3})^2}{2^3+2}$ , apply the order of operations to fully resolve the numerator and denominator independently.

First, simplify the numerator by evaluating the exponent on the fraction: $\left(\frac{1}{3}\right)^2 = \frac{1}{9}$ . Next, simplify the denominator by evaluating its exponent to get $2^3 = 8$ , and then add $2$ to yield $8 + 2 = 10$ . Finally, divide the numerator by the denominator: $\frac{1}{9} \div 10 = \frac{1}{9} \cdot \frac{1}{10} = \frac{1}{90}$ . The overall simplified result is $\frac{1}{90}$ .