Solve -(-3x^{5}y^{4})^{2}-x^12y^10:(-1/5x^2y^2)

$$- ( - 3 x ^ { 5 } y ^ { 4 } ) ^ { 2 } - x ^ { 12 } y ^ { 10 } : ( - \frac { 1 } { 5 } x ^ { 2 } y ^ { 2 } )$$

Evaluate

$$-4y^{8}x^{10}$$

Solution Steps

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

$$-\left(-3\right)^{2}\left(x^{5}\right)^{2}\left(y^{4}\right)^{2}-\frac{x^{12}y^{10}}{-\frac{1}{5}x^{2}y^{2}}$$

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

$$-\left(-3\right)^{2}x^{10}\left(y^{4}\right)^{2}-\frac{x^{12}y^{10}}{-\frac{1}{5}x^{2}y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$-\left(-3\right)^{2}x^{10}y^{8}-\frac{x^{12}y^{10}}{-\frac{1}{5}x^{2}y^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$-9x^{10}y^{8}-\frac{x^{12}y^{10}}{-\frac{1}{5}x^{2}y^{2}}$$

Cancel out x^{2}y^{2} in both numerator and denominator.

$$-9x^{10}y^{8}-\frac{y^{8}x^{10}}{-\frac{1}{5}}$$

Divide y^{8}x^{10} by -\frac{1}{5} by multiplying y^{8}x^{10} by the reciprocal of -\frac{1}{5}.

$$-9x^{10}y^{8}-\frac{y^{8}x^{10}\times 5}{-1}$$

Anything divided by -1 gives its opposite.

$$-9x^{10}y^{8}-\left(-y^{8}x^{10}\times 5\right)$$

Multiply -1 and -1 to get 1.

$$-9x^{10}y^{8}+y^{8}x^{10}\times 5$$

Combine -9x^{10}y^{8} and y^{8}x^{10}\times 5 to get -4x^{10}y^{8}.

$$-4x^{10}y^{8}$$

Expand

$$-4y^{8}x^{10}$$

Solution Steps

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

$$-\left(-3\right)^{2}\left(x^{5}\right)^{2}\left(y^{4}\right)^{2}-\frac{x^{12}y^{10}}{-\frac{1}{5}x^{2}y^{2}}$$

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

$$-\left(-3\right)^{2}x^{10}\left(y^{4}\right)^{2}-\frac{x^{12}y^{10}}{-\frac{1}{5}x^{2}y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$-\left(-3\right)^{2}x^{10}y^{8}-\frac{x^{12}y^{10}}{-\frac{1}{5}x^{2}y^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$-9x^{10}y^{8}-\frac{x^{12}y^{10}}{-\frac{1}{5}x^{2}y^{2}}$$

Cancel out x^{2}y^{2} in both numerator and denominator.

$$-9x^{10}y^{8}-\frac{y^{8}x^{10}}{-\frac{1}{5}}$$

Divide y^{8}x^{10} by -\frac{1}{5} by multiplying y^{8}x^{10} by the reciprocal of -\frac{1}{5}.

$$-9x^{10}y^{8}-\frac{y^{8}x^{10}\times 5}{-1}$$

Anything divided by -1 gives its opposite.

$$-9x^{10}y^{8}-\left(-y^{8}x^{10}\times 5\right)$$

Multiply -1 and -1 to get 1.

$$-9x^{10}y^{8}+y^{8}x^{10}\times 5$$

Combine -9x^{10}y^{8} and y^{8}x^{10}\times 5 to get -4x^{10}y^{8}.

$$-4x^{10}y^{8}$$