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

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

Evaluate

$$-x^{7}y^{18}$$

Short Solution Steps

To raise \frac{-x^{3}}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(-x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}}\times \left(\frac{-x^{-4}}{x^{4}y^{6}}\right)^{-2}$$

To raise \frac{-x^{-4}}{x^{4}y^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}}\times \frac{\left(-x^{-4}\right)^{-2}}{\left(x^{4}y^{6}\right)^{-2}}$$

Multiply \frac{\left(-x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}} times \frac{\left(-x^{-4}\right)^{-2}}{\left(x^{4}y^{6}\right)^{-2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{\left(y^{2}\right)^{-3}\left(x^{4}y^{6}\right)^{-2}}$$

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

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-6}\left(x^{4}y^{6}\right)^{-2}}$$

Expand \left(x^{4}y^{6}\right)^{-2}.

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-6}\left(x^{4}\right)^{-2}\left(y^{6}\right)^{-2}}$$

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

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-6}x^{-8}\left(y^{6}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-6}x^{-8}y^{-12}}$$

To multiply powers of the same base, add their exponents. Add -6 and -12 to get -18.

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

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

$$\frac{\left(-1\right)^{-3}\left(x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\left(-1\right)^{-3}x^{-9}\left(-x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

Calculate -1 to the power of -3 and get -1.

$$\frac{-x^{-9}\left(-x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

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

$$\frac{-x^{-9}\left(-1\right)^{-2}\left(x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

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

$$\frac{-x^{-9}\left(-1\right)^{-2}x^{8}}{y^{-18}x^{-8}}$$

Calculate -1 to the power of -2 and get 1.

$$\frac{-x^{-9}x^{8}}{y^{-18}x^{-8}}$$

To multiply powers of the same base, add their exponents. Add -9 and 8 to get -1.

$$\frac{-x^{-1}}{y^{-18}x^{-8}}$$

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

$$\frac{-x^{7}}{y^{-18}}$$

Expand

$$-x^{7}y^{18}$$

Short Solution Steps

To raise \frac{-x^{3}}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(-x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}}\times \left(\frac{-x^{-4}}{x^{4}y^{6}}\right)^{-2}$$

To raise \frac{-x^{-4}}{x^{4}y^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}}\times \frac{\left(-x^{-4}\right)^{-2}}{\left(x^{4}y^{6}\right)^{-2}}$$

Multiply \frac{\left(-x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}} times \frac{\left(-x^{-4}\right)^{-2}}{\left(x^{4}y^{6}\right)^{-2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{\left(y^{2}\right)^{-3}\left(x^{4}y^{6}\right)^{-2}}$$

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

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-6}\left(x^{4}y^{6}\right)^{-2}}$$

Expand \left(x^{4}y^{6}\right)^{-2}.

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-6}\left(x^{4}\right)^{-2}\left(y^{6}\right)^{-2}}$$

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

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-6}x^{-8}\left(y^{6}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-6}x^{-8}y^{-12}}$$

To multiply powers of the same base, add their exponents. Add -6 and -12 to get -18.

$$\frac{\left(-x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

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

$$\frac{\left(-1\right)^{-3}\left(x^{3}\right)^{-3}\left(-x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\left(-1\right)^{-3}x^{-9}\left(-x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

Calculate -1 to the power of -3 and get -1.

$$\frac{-x^{-9}\left(-x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

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

$$\frac{-x^{-9}\left(-1\right)^{-2}\left(x^{-4}\right)^{-2}}{y^{-18}x^{-8}}$$

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

$$\frac{-x^{-9}\left(-1\right)^{-2}x^{8}}{y^{-18}x^{-8}}$$

Calculate -1 to the power of -2 and get 1.

$$\frac{-x^{-9}x^{8}}{y^{-18}x^{-8}}$$

To multiply powers of the same base, add their exponents. Add -9 and 8 to get -1.

$$\frac{-x^{-1}}{y^{-18}x^{-8}}$$

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

$$\frac{-x^{7}}{y^{-18}}$$