Solve (frac{4x^{-3}y^-2}{12x^-1y^-5})^-3

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

Evaluate

$$\frac{27x^{6}}{y^{9}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{y^{-9}}{3^{-3}x^{-6}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{y^{-9}}{\frac{1}{27}x^{-6}}$$

Expand

$$\frac{27x^{6}}{y^{9}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{y^{-9}}{3^{-3}x^{-6}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{y^{-9}}{\frac{1}{27}x^{-6}}$$