Solve (4x^3)^2/(-2x^5)^3

$$\frac { ( 4 x ^ { 3 } ) ^ { 2 } } { ( - 2 x ^ { 5 } ) ^ { 3 } }$$

Evaluate

$$-\frac{2}{x^{9}}$$

Solution Steps

Expand \left(4x^{3}\right)^{2}.

$$\frac{4^{2}\left(x^{3}\right)^{2}}{\left(-2x^{5}\right)^{3}}$$

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

$$\frac{4^{2}x^{6}}{\left(-2x^{5}\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{6}}{\left(-2x^{5}\right)^{3}}$$

Expand \left(-2x^{5}\right)^{3}.

$$\frac{16x^{6}}{\left(-2\right)^{3}\left(x^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{16x^{6}}{\left(-2\right)^{3}x^{15}}$$

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

$$\frac{16x^{6}}{-8x^{15}}$$

Cancel out 8x^{6} in both numerator and denominator.

$$\frac{2}{-x^{9}}$$

Expand

$$-\frac{2}{x^{9}}$$

Solution Steps

Expand \left(4x^{3}\right)^{2}.

$$\frac{4^{2}\left(x^{3}\right)^{2}}{\left(-2x^{5}\right)^{3}}$$

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

$$\frac{4^{2}x^{6}}{\left(-2x^{5}\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{6}}{\left(-2x^{5}\right)^{3}}$$

Expand \left(-2x^{5}\right)^{3}.

$$\frac{16x^{6}}{\left(-2\right)^{3}\left(x^{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{16x^{6}}{\left(-2\right)^{3}x^{15}}$$

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

$$\frac{16x^{6}}{-8x^{15}}$$

Cancel out 8x^{6} in both numerator and denominator.

$$\frac{2}{-x^{9}}$$