Solve (-2x^{3}y^2)^5(x^7y/8y^6)

$$( - 2 x ^ { 3 } y ^ { 2 } ) ^ { 5 } ( \frac { x ^ { 7 } y } { 8 y ^ { 6 } } )$$

Evaluate

$$-4y^{5}x^{22}$$

Solution Steps

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

$$\left(-2\right)^{5}\left(x^{3}\right)^{5}\left(y^{2}\right)^{5}\times \frac{x^{7}y}{8y^{6}}$$

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

$$\left(-2\right)^{5}x^{15}\left(y^{2}\right)^{5}\times \frac{x^{7}y}{8y^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(-2\right)^{5}x^{15}y^{10}\times \frac{x^{7}y}{8y^{6}}$$

Calculate -2 to the power of 5 and get -32.

$$-32x^{15}y^{10}\times \frac{x^{7}y}{8y^{6}}$$

Cancel out y in both numerator and denominator.

$$-32x^{15}y^{10}\times \frac{x^{7}}{8y^{5}}$$

Express -32\times \frac{x^{7}}{8y^{5}} as a single fraction.

$$\frac{-32x^{7}}{8y^{5}}x^{15}y^{10}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-4x^{7}}{y^{5}}x^{15}y^{10}$$

Express \frac{-4x^{7}}{y^{5}}x^{15} as a single fraction.

$$\frac{-4x^{7}x^{15}}{y^{5}}y^{10}$$

Express \frac{-4x^{7}x^{15}}{y^{5}}y^{10} as a single fraction.

$$\frac{-4x^{7}x^{15}y^{10}}{y^{5}}$$

Cancel out y^{5} in both numerator and denominator.

$$-4y^{5}x^{7}x^{15}$$

To multiply powers of the same base, add their exponents. Add 7 and 15 to get 22.

$$-4y^{5}x^{22}$$

Expand

$$-4y^{5}x^{22}$$

Solution Steps

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

$$\left(-2\right)^{5}\left(x^{3}\right)^{5}\left(y^{2}\right)^{5}\times \frac{x^{7}y}{8y^{6}}$$

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

$$\left(-2\right)^{5}x^{15}\left(y^{2}\right)^{5}\times \frac{x^{7}y}{8y^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(-2\right)^{5}x^{15}y^{10}\times \frac{x^{7}y}{8y^{6}}$$

Calculate -2 to the power of 5 and get -32.

$$-32x^{15}y^{10}\times \frac{x^{7}y}{8y^{6}}$$

Cancel out y in both numerator and denominator.

$$-32x^{15}y^{10}\times \frac{x^{7}}{8y^{5}}$$

Express -32\times \frac{x^{7}}{8y^{5}} as a single fraction.

$$\frac{-32x^{7}}{8y^{5}}x^{15}y^{10}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-4x^{7}}{y^{5}}x^{15}y^{10}$$

Express \frac{-4x^{7}}{y^{5}}x^{15} as a single fraction.

$$\frac{-4x^{7}x^{15}}{y^{5}}y^{10}$$

Express \frac{-4x^{7}x^{15}}{y^{5}}y^{10} as a single fraction.

$$\frac{-4x^{7}x^{15}y^{10}}{y^{5}}$$

Cancel out y^{5} in both numerator and denominator.

$$-4y^{5}x^{7}x^{15}$$

To multiply powers of the same base, add their exponents. Add 7 and 15 to get 22.

$$-4y^{5}x^{22}$$