Solve E=(-x^{2})^{3}(-x^{-3})^2(x^3)(x^-3)(-x^(-3))

$$E = ( - x ^ { 2 } ) ^ { 3 } ( - x ^ { - 3 } ) ^ { 2 } ( x ^ { 3 } ) ( x ^ { - 3 } ) ( - x ^ { ( - 3 ) } )$$

Solve for E

$$E=\frac{1}{x^{3}}$$

$$x\neq 0$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$E=\left(-x^{2}\right)^{3}\left(-x^{-3}\right)^{3}x^{3}x^{-3}$$

Expand \left(-x^{2}\right)^{3}.

$$E=\left(-1\right)^{3}\left(x^{2}\right)^{3}\left(-x^{-3}\right)^{3}x^{3}x^{-3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$E=\left(-1\right)^{3}x^{6}\left(-x^{-3}\right)^{3}x^{3}x^{-3}$$

Calculate -1 to the power of 3 and get -1.

$$E=-x^{6}\left(-x^{-3}\right)^{3}x^{3}x^{-3}$$

Expand \left(-x^{-3}\right)^{3}.

$$E=-x^{6}\left(-1\right)^{3}\left(x^{-3}\right)^{3}x^{3}x^{-3}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$E=-x^{6}\left(-1\right)^{3}x^{-9}x^{3}x^{-3}$$

Calculate -1 to the power of 3 and get -1.

$$E=-x^{6}\left(-1\right)x^{-9}x^{3}x^{-3}$$

Multiply -1 and -1 to get 1.

$$E=x^{6}x^{-9}x^{3}x^{-3}$$

To multiply powers of the same base, add their exponents. Add 6 and -9 to get -3.

$$E=x^{-3}x^{3}x^{-3}$$

To multiply powers of the same base, add their exponents. Add -3 and -3 to get -6.

$$E=x^{-6}x^{3}$$

To multiply powers of the same base, add their exponents. Add -6 and 3 to get -3.

$$E=x^{-3}$$

Solve for x (complex solution)

$$x=e^{\frac{2\pi i}{3}}E^{-\frac{1}{3}}$$

$$x=E^{-\frac{1}{3}}$$

$$x=e^{\frac{4\pi i}{3}}E^{-\frac{1}{3}}\text{, }E\neq 0$$

Solve for x

$$x=\frac{1}{\sqrt[3]{E}}$$

$$E\neq 0$$