Solve frac{(-4x^{5}y^-2)^3}{x^7y^-3}=

$$\frac { ( - 4 x ^ { 5 } y ^ { - 2 } ) ^ { 3 } } { x ^ { 7 } y ^ { - 3 } } =$$

Evaluate

$$-\frac{64x^{8}}{y^{3}}$$

Solution Steps

Expand \left(-4x^{5}y^{-2}\right)^{3}.

$$\frac{\left(-4\right)^{3}\left(x^{5}\right)^{3}\left(y^{-2}\right)^{3}}{x^{7}y^{-3}}$$

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

$$\frac{\left(-4\right)^{3}x^{15}\left(y^{-2}\right)^{3}}{x^{7}y^{-3}}$$

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

$$\frac{\left(-4\right)^{3}x^{15}y^{-6}}{x^{7}y^{-3}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{-64x^{15}y^{-6}}{x^{7}y^{-3}}$$

Cancel out x^{7} in both numerator and denominator.

$$\frac{-64y^{-6}x^{8}}{y^{-3}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{-64x^{8}}{y^{3}}$$

Expand

$$-\frac{64x^{8}}{y^{3}}$$

Solution Steps

Expand \left(-4x^{5}y^{-2}\right)^{3}.

$$\frac{\left(-4\right)^{3}\left(x^{5}\right)^{3}\left(y^{-2}\right)^{3}}{x^{7}y^{-3}}$$

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

$$\frac{\left(-4\right)^{3}x^{15}\left(y^{-2}\right)^{3}}{x^{7}y^{-3}}$$

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

$$\frac{\left(-4\right)^{3}x^{15}y^{-6}}{x^{7}y^{-3}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{-64x^{15}y^{-6}}{x^{7}y^{-3}}$$

Cancel out x^{7} in both numerator and denominator.

$$\frac{-64y^{-6}x^{8}}{y^{-3}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{-64x^{8}}{y^{3}}$$