Solve (-2/3)^4+(-2/3)^3=(-3/2)^11

$$( \frac { - 2 } { 3 } ) ^ { 4 } + ( \frac { - 2 } { 3 } ) ^ { 3 } = ( \frac { - 3 } { 2 } ) ^ { 11 }$$

Verify

Solution Steps

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\left(-\frac{2}{3}\right)^{4}+\left(\frac{-2}{3}\right)^{3}=\left(\frac{-3}{2}\right)^{11}$$

Calculate -\frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{16}{81}+\left(\frac{-2}{3}\right)^{3}=\left(\frac{-3}{2}\right)^{11}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{16}{81}+\left(-\frac{2}{3}\right)^{3}=\left(\frac{-3}{2}\right)^{11}$$

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$\frac{16}{81}-\frac{8}{27}=\left(\frac{-3}{2}\right)^{11}$$

Subtract \frac{8}{27} from \frac{16}{81} to get -\frac{8}{81}.

$$-\frac{8}{81}=\left(\frac{-3}{2}\right)^{11}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-\frac{8}{81}=\left(-\frac{3}{2}\right)^{11}$$

Calculate -\frac{3}{2} to the power of 11 and get -\frac{177147}{2048}.

$$-\frac{8}{81}=-\frac{177147}{2048}$$

Least common multiple of 81 and 2048 is 165888. Convert -\frac{8}{81} and -\frac{177147}{2048} to fractions with denominator 165888.

$$-\frac{16384}{165888}=-\frac{14348907}{165888}$$

Compare -\frac{16384}{165888} and -\frac{14348907}{165888}.

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