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

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

Evaluate

$$-\frac{y^{9}}{125x^{6}}$$

Solution Steps

To raise \frac{y^{3}}{-5x^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{y^{9}}{\left(-5x^{2}\right)^{3}}$$

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

$$\frac{y^{9}}{\left(-5\right)^{3}\left(x^{2}\right)^{3}}$$

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

$$\frac{y^{9}}{\left(-5\right)^{3}x^{6}}$$

Calculate -5 to the power of 3 and get -125.

$$\frac{y^{9}}{-125x^{6}}$$

Expand

$$-\frac{y^{9}}{125x^{6}}$$

Solution Steps

To raise \frac{y^{3}}{-5x^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{y^{9}}{\left(-5x^{2}\right)^{3}}$$

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

$$\frac{y^{9}}{\left(-5\right)^{3}\left(x^{2}\right)^{3}}$$

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

$$\frac{y^{9}}{\left(-5\right)^{3}x^{6}}$$

Calculate -5 to the power of 3 and get -125.

$$\frac{y^{9}}{-125x^{6}}$$