Solve (-2/3)^3:4/27-(sqrt{64/49}*21/4-5^2)

$$( \frac { - 2 } { 3 } ) ^ { 3 } : \frac { 4 } { 27 } - ( \sqrt { \frac { 64 } { 49 } } \cdot \frac { 21 } { 4 } - 5 ^ { 2 } )$$

Evaluate

$$17$$

Solution Steps

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

$$\frac{\left(-\frac{2}{3}\right)^{3}}{\frac{4}{27}}-\left(\sqrt{\frac{64}{49}}\times \frac{21}{4}-5^{2}\right)$$

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

$$\frac{-\frac{8}{27}}{\frac{4}{27}}-\left(\sqrt{\frac{64}{49}}\times \frac{21}{4}-5^{2}\right)$$

Divide -\frac{8}{27} by \frac{4}{27} by multiplying -\frac{8}{27} by the reciprocal of \frac{4}{27}.

$$-\frac{8}{27}\times \frac{27}{4}-\left(\sqrt{\frac{64}{49}}\times \frac{21}{4}-5^{2}\right)$$

Multiply -\frac{8}{27} and \frac{27}{4} to get -2.

$$-2-\left(\sqrt{\frac{64}{49}}\times \frac{21}{4}-5^{2}\right)$$

Rewrite the square root of the division \frac{64}{49} as the division of square roots \frac{\sqrt{64}}{\sqrt{49}}. Take the square root of both numerator and denominator.

$$-2-\left(\frac{8}{7}\times \frac{21}{4}-5^{2}\right)$$

Multiply \frac{8}{7} and \frac{21}{4} to get 6.

$$-2-\left(6-5^{2}\right)$$

Calculate 5 to the power of 2 and get 25.

$$-2-\left(6-25\right)$$

Subtract 25 from 6 to get -19.

$$-2-\left(-19\right)$$

The opposite of -19 is 19.

$$-2+19$$

Add -2 and 19 to get 17.

$$17$$

Factor

$$17$$