Solve (-2x)^3*x^6div(-3x^3)^2

$$( - 2 x ) ^ { 3 } \cdot x ^ { 6 } \div ( - 3 x ^ { 3 } ) ^ { 2 }$$

Evaluate

$$-\frac{8x^{3}}{9}$$

Solution Steps

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

$$\frac{\left(-2\right)^{3}x^{3}x^{6}}{\left(-3x^{3}\right)^{2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8x^{3}x^{6}}{\left(-3x^{3}\right)^{2}}$$

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

$$\frac{-8x^{9}}{\left(-3x^{3}\right)^{2}}$$

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

$$\frac{-8x^{9}}{\left(-3\right)^{2}\left(x^{3}\right)^{2}}$$

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

$$\frac{-8x^{9}}{\left(-3\right)^{2}x^{6}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{-8x^{9}}{9x^{6}}$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{-8x^{3}}{9}$$

Expand

$$-\frac{8x^{3}}{9}$$

Solution Steps

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

$$\frac{\left(-2\right)^{3}x^{3}x^{6}}{\left(-3x^{3}\right)^{2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{-8x^{3}x^{6}}{\left(-3x^{3}\right)^{2}}$$

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

$$\frac{-8x^{9}}{\left(-3x^{3}\right)^{2}}$$

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

$$\frac{-8x^{9}}{\left(-3\right)^{2}\left(x^{3}\right)^{2}}$$

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

$$\frac{-8x^{9}}{\left(-3\right)^{2}x^{6}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{-8x^{9}}{9x^{6}}$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{-8x^{3}}{9}$$