Solve (frac{(-6x^{-2}y)(-9x^{-5}y^-2)}{3x^2y^-4})^3

$$( \frac { ( - 6 x ^ { - 2 } y ) ( - 9 x ^ { - 5 } y ^ { - 2 } ) } { 3 x ^ { 2 } y ^ { - 4 } } ) ^ { 3 }$$

Evaluate

$$\frac{5832y^{9}}{x^{27}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and -5 to get -7.

$$\left(\frac{-6x^{-7}y\left(-9\right)y^{-2}}{3x^{2}y^{-4}}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\left(\frac{-6x^{-7}y^{-1}\left(-9\right)}{3x^{2}y^{-4}}\right)^{3}$$

Cancel out 3 in both numerator and denominator.

$$\left(\frac{-9\left(-2\right)x^{-7}\times \frac{1}{y}}{y^{-4}x^{2}}\right)^{3}$$

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

$$\left(\frac{-9\left(-2\right)x^{-7}y^{3}}{x^{2}}\right)^{3}$$

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

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

Multiply -9 and -2 to get 18.

$$\left(\frac{18y^{3}}{x^{9}}\right)^{3}$$

To raise \frac{18y^{3}}{x^{9}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(18y^{3}\right)^{3}}{\left(x^{9}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{\left(18y^{3}\right)^{3}}{x^{27}}$$

Expand \left(18y^{3}\right)^{3}.

$$\frac{18^{3}\left(y^{3}\right)^{3}}{x^{27}}$$

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

$$\frac{18^{3}y^{9}}{x^{27}}$$

Calculate 18 to the power of 3 and get 5832.

$$\frac{5832y^{9}}{x^{27}}$$

Expand

$$\frac{5832y^{9}}{x^{27}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and -5 to get -7.

$$\left(\frac{-6x^{-7}y\left(-9\right)y^{-2}}{3x^{2}y^{-4}}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\left(\frac{-6x^{-7}y^{-1}\left(-9\right)}{3x^{2}y^{-4}}\right)^{3}$$

Cancel out 3 in both numerator and denominator.

$$\left(\frac{-9\left(-2\right)x^{-7}\times \frac{1}{y}}{y^{-4}x^{2}}\right)^{3}$$

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

$$\left(\frac{-9\left(-2\right)x^{-7}y^{3}}{x^{2}}\right)^{3}$$

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

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

Multiply -9 and -2 to get 18.

$$\left(\frac{18y^{3}}{x^{9}}\right)^{3}$$

To raise \frac{18y^{3}}{x^{9}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(18y^{3}\right)^{3}}{\left(x^{9}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{\left(18y^{3}\right)^{3}}{x^{27}}$$

Expand \left(18y^{3}\right)^{3}.

$$\frac{18^{3}\left(y^{3}\right)^{3}}{x^{27}}$$

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

$$\frac{18^{3}y^{9}}{x^{27}}$$

Calculate 18 to the power of 3 and get 5832.

$$\frac{5832y^{9}}{x^{27}}$$