Solve left(-3^6*-3^2right)^3-3-3^-4

$${ \left( { -3 }^{ 6 } \times { -3 }^{ 2 } \right) }^{ 3 } -3 { -3 }^{ -4 }$$

Evaluate

$$\frac{7625597484986}{27}\approx 282429536480.962962963$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\left(\left(-3\right)^{8}\right)^{3}-3\left(-3\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\left(-3\right)^{24}-3\left(-3\right)^{-4}$$

Calculate -3 to the power of 24 and get 282429536481.

$$282429536481-3\left(-3\right)^{-4}$$

Calculate -3 to the power of -4 and get \frac{1}{81}.

$$282429536481-3\times \frac{1}{81}$$

Multiply 3 and \frac{1}{81} to get \frac{1}{27}.

$$282429536481-\frac{1}{27}$$

Subtract \frac{1}{27} from 282429536481 to get \frac{7625597484986}{27}.

$$\frac{7625597484986}{27}$$

Factor

$$\frac{2 \cdot 13 \cdot 109 \cdot 433 \cdot 757 \cdot 8209}{3 ^ {3}} = 282429536480\frac{26}{27} = 282429536480.96295$$