Solve frac{-2(p^{-4}y^4)^-3}{6p^-3y^-1}

$$\frac { - 2 ( p ^ { - 4 } y ^ { 4 } ) ^ { - 3 } } { 6 p ^ { - 3 } y ^ { - 1 } }$$

Evaluate

$$-\frac{p^{15}}{3y^{11}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{-\left(p^{-4}y^{4}\right)^{-3}}{3p^{-3}\times \frac{1}{y}}$$

Expand \left(p^{-4}y^{4}\right)^{-3}.

$$\frac{-\left(p^{-4}\right)^{-3}\left(y^{4}\right)^{-3}}{3p^{-3}\times \frac{1}{y}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -3 to get 12.

$$\frac{-p^{12}\left(y^{4}\right)^{-3}}{3p^{-3}\times \frac{1}{y}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{-p^{12}y^{-12}}{3p^{-3}\times \frac{1}{y}}$$

Express 3\times \frac{1}{y} as a single fraction.

$$\frac{-p^{12}y^{-12}}{\frac{3}{y}p^{-3}}$$

Express \frac{3}{y}p^{-3} as a single fraction.

$$\frac{-p^{12}y^{-12}}{\frac{3p^{-3}}{y}}$$

Divide -p^{12}y^{-12} by \frac{3p^{-3}}{y} by multiplying -p^{12}y^{-12} by the reciprocal of \frac{3p^{-3}}{y}.

$$\frac{-p^{12}y^{-12}y}{3p^{-3}}$$

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

$$\frac{-y^{-12}yp^{15}}{3}$$

To multiply powers of the same base, add their exponents. Add -12 and 1 to get -11.

$$\frac{-y^{-11}p^{15}}{3}$$

Expand

$$-\frac{p^{15}}{3y^{11}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{-\left(p^{-4}y^{4}\right)^{-3}}{3p^{-3}\times \frac{1}{y}}$$

Expand \left(p^{-4}y^{4}\right)^{-3}.

$$\frac{-\left(p^{-4}\right)^{-3}\left(y^{4}\right)^{-3}}{3p^{-3}\times \frac{1}{y}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -3 to get 12.

$$\frac{-p^{12}\left(y^{4}\right)^{-3}}{3p^{-3}\times \frac{1}{y}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -3 to get -12.

$$\frac{-p^{12}y^{-12}}{3p^{-3}\times \frac{1}{y}}$$

Express 3\times \frac{1}{y} as a single fraction.

$$\frac{-p^{12}y^{-12}}{\frac{3}{y}p^{-3}}$$

Express \frac{3}{y}p^{-3} as a single fraction.

$$\frac{-p^{12}y^{-12}}{\frac{3p^{-3}}{y}}$$

Divide -p^{12}y^{-12} by \frac{3p^{-3}}{y} by multiplying -p^{12}y^{-12} by the reciprocal of \frac{3p^{-3}}{y}.

$$\frac{-p^{12}y^{-12}y}{3p^{-3}}$$

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

$$\frac{-y^{-12}yp^{15}}{3}$$

To multiply powers of the same base, add their exponents. Add -12 and 1 to get -11.

$$\frac{-y^{-11}p^{15}}{3}$$