Solve (-4/7)^3=(-7/4)^3=-343/64

$$( - \frac { 4 } { 7 } ) ^ { 3 } = ( - \frac { 7 } { 4 } ) ^ { 3 } = - \frac { 343 } { 64 }$$

Verify

Solution Steps

Calculate -\frac{4}{7} to the power of 3 and get -\frac{64}{343}.

$$-\frac{64}{343}=\left(-\frac{7}{4}\right)^{3}\text{ and }\left(-\frac{7}{4}\right)^{3}=-\frac{343}{64}$$

Calculate -\frac{7}{4} to the power of 3 and get -\frac{343}{64}.

$$-\frac{64}{343}=-\frac{343}{64}\text{ and }\left(-\frac{7}{4}\right)^{3}=-\frac{343}{64}$$

Least common multiple of 343 and 64 is 21952. Convert -\frac{64}{343} and -\frac{343}{64} to fractions with denominator 21952.

$$-\frac{4096}{21952}=-\frac{117649}{21952}\text{ and }\left(-\frac{7}{4}\right)^{3}=-\frac{343}{64}$$

Compare -\frac{4096}{21952} and -\frac{117649}{21952}.

$$\text{false}\text{ and }\left(-\frac{7}{4}\right)^{3}=-\frac{343}{64}$$

Calculate -\frac{7}{4} to the power of 3 and get -\frac{343}{64}.

$$\text{false}\text{ and }-\frac{343}{64}=-\frac{343}{64}$$

Compare -\frac{343}{64} and -\frac{343}{64}.

$$\text{false}\text{ and }\text{true}$$

The conjunction of \text{false} and \text{true} is \text{false}.

$$\text{false}$$