Solve (-2xy^2)^5(x^7/8y^3)=

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

Evaluate

$$-4y^{7}x^{12}$$

Solution Steps

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

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

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

$$\left(-2\right)^{5}x^{5}y^{10}\times \frac{x^{7}}{8y^{3}}$$

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

$$-32x^{5}y^{10}\times \frac{x^{7}}{8y^{3}}$$

Express -32\times \frac{x^{7}}{8y^{3}} as a single fraction.

$$\frac{-32x^{7}}{8y^{3}}x^{5}y^{10}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-4x^{7}}{y^{3}}x^{5}y^{10}$$

Express \frac{-4x^{7}}{y^{3}}x^{5} as a single fraction.

$$\frac{-4x^{7}x^{5}}{y^{3}}y^{10}$$

Express \frac{-4x^{7}x^{5}}{y^{3}}y^{10} as a single fraction.

$$\frac{-4x^{7}x^{5}y^{10}}{y^{3}}$$

Cancel out y^{3} in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$-4x^{12}y^{7}$$

Expand

$$-4y^{7}x^{12}$$

Solution Steps

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

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

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

$$\left(-2\right)^{5}x^{5}y^{10}\times \frac{x^{7}}{8y^{3}}$$

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

$$-32x^{5}y^{10}\times \frac{x^{7}}{8y^{3}}$$

Express -32\times \frac{x^{7}}{8y^{3}} as a single fraction.

$$\frac{-32x^{7}}{8y^{3}}x^{5}y^{10}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-4x^{7}}{y^{3}}x^{5}y^{10}$$

Express \frac{-4x^{7}}{y^{3}}x^{5} as a single fraction.

$$\frac{-4x^{7}x^{5}}{y^{3}}y^{10}$$

Express \frac{-4x^{7}x^{5}}{y^{3}}y^{10} as a single fraction.

$$\frac{-4x^{7}x^{5}y^{10}}{y^{3}}$$

Cancel out y^{3} in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$-4x^{12}y^{7}$$