Solve (frac{6x^{4}y^-2}{12xy^3z^-1})^-3=

$$( \frac { 6 x ^ { 4 } y ^ { - 2 } } { 12 x y ^ { 3 } z ^ { - 1 } } ) ^ { - 3 } =$$

Evaluate

$$\frac{8y^{15}}{z^{3}x^{9}}$$

Solution Steps

Cancel out 6x in both numerator and denominator.

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

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

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

Express 2\times \frac{1}{z} as a single fraction.

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

Express \frac{2}{z}y^{5} as a single fraction.

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

Divide x^{3} by \frac{2y^{5}}{z} by multiplying x^{3} by the reciprocal of \frac{2y^{5}}{z}.

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

To raise \frac{x^{3}z}{2y^{5}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$\frac{x^{-9}z^{-3}}{\left(2y^{5}\right)^{-3}}$$

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

$$\frac{x^{-9}z^{-3}}{2^{-3}\left(y^{5}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{x^{-9}z^{-3}}{2^{-3}y^{-15}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{x^{-9}z^{-3}}{\frac{1}{8}y^{-15}}$$

Expand

$$\frac{8y^{15}}{z^{3}x^{9}}$$

Solution Steps

Cancel out 6x in both numerator and denominator.

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

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

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

Express 2\times \frac{1}{z} as a single fraction.

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

Express \frac{2}{z}y^{5} as a single fraction.

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

Divide x^{3} by \frac{2y^{5}}{z} by multiplying x^{3} by the reciprocal of \frac{2y^{5}}{z}.

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

To raise \frac{x^{3}z}{2y^{5}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$\frac{x^{-9}z^{-3}}{\left(2y^{5}\right)^{-3}}$$

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

$$\frac{x^{-9}z^{-3}}{2^{-3}\left(y^{5}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{x^{-9}z^{-3}}{2^{-3}y^{-15}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{x^{-9}z^{-3}}{\frac{1}{8}y^{-15}}$$