Solve 3^4*(-2/3)^3+1/(-0,1)^3

$$3 ^ { 4 } \cdot ( - \frac { 2 } { 3 } ) ^ { 3 } + \frac { 1 } { ( - 0,1 ) ^ { 3 } }$$

Evaluate

$$-1024$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$81\left(-\frac{2}{3}\right)^{3}+\frac{1}{\left(-0,1\right)^{3}}$$

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

$$81\left(-\frac{8}{27}\right)+\frac{1}{\left(-0,1\right)^{3}}$$

Express 81\left(-\frac{8}{27}\right) as a single fraction.

$$\frac{81\left(-8\right)}{27}+\frac{1}{\left(-0,1\right)^{3}}$$

Multiply 81 and -8 to get -648.

$$\frac{-648}{27}+\frac{1}{\left(-0,1\right)^{3}}$$

Divide -648 by 27 to get -24.

$$-24+\frac{1}{\left(-0,1\right)^{3}}$$

Calculate -0,1 to the power of 3 and get -0,001.

$$-24+\frac{1}{-0,001}$$

Expand \frac{1}{-0,001} by multiplying both numerator and the denominator by 1000.

$$-24+\frac{1000}{-1}$$

Fraction \frac{1000}{-1} can be rewritten as -1000 by extracting the negative sign.

$$-24-1000$$

Subtract 1000 from -24 to get -1024.

$$-1024$$

Factor

$$-1024$$