Solve (2/3)^-1=(2/4)^-2+(1/2)^2

$$( \frac { 2 } { 3 } ) ^ { - 1 } = ( \frac { 2 } { 4 } ) ^ { - 2 } + ( \frac { 1 } { 2 } ) ^ { 2 }$$

Verify

Solution Steps

Calculate \frac{2}{3} to the power of -1 and get \frac{3}{2}.

$$\frac{3}{2}=\left(\frac{2}{4}\right)^{-2}+\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}=\left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of -2 and get 4.

$$\frac{3}{2}=4+\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{3}{2}=4+\frac{1}{4}$$

Add 4 and \frac{1}{4} to get \frac{17}{4}.

$$\frac{3}{2}=\frac{17}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{17}{4} to fractions with denominator 4.

$$\frac{6}{4}=\frac{17}{4}$$

Compare \frac{6}{4} and \frac{17}{4}.

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