Solve [(frac{x^{-5}y^{-2}z^{-1}}{x^{2}y^frac{1{3}}z^-3})^-2]^3

$$[ ( \frac { x ^ { - 5 } y ^ { - 2 } z ^ { - 1 } } { x ^ { 2 } y ^ { \frac { 1 } { 3 } } z ^ { - 3 } } ) ^ { - 2 } ] ^ { 3 }$$

Evaluate

$$\frac{y^{14}x^{42}}{z^{12}}$$

Solution Steps

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

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

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

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

To raise \frac{z^{2}}{y^{\frac{7}{3}}x^{7}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{\left(z^{2}\right)^{-2}}{\left(y^{\frac{7}{3}}x^{7}\right)^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$\frac{z^{-12}}{\left(\left(y^{\frac{7}{3}}x^{7}\right)^{-2}\right)^{3}}$$

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

$$\frac{z^{-12}}{\left(y^{\frac{7}{3}}x^{7}\right)^{-6}}$$

Expand \left(y^{\frac{7}{3}}x^{7}\right)^{-6}.

$$\frac{z^{-12}}{\left(y^{\frac{7}{3}}\right)^{-6}\left(x^{7}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{3} and -6 to get -14.

$$\frac{z^{-12}}{y^{-14}\left(x^{7}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -6 to get -42.

$$\frac{z^{-12}}{y^{-14}x^{-42}}$$

Expand

$$\frac{y^{14}x^{42}}{z^{12}}$$

Solution Steps

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

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

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

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

To raise \frac{z^{2}}{y^{\frac{7}{3}}x^{7}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{\left(z^{2}\right)^{-2}}{\left(y^{\frac{7}{3}}x^{7}\right)^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$\frac{z^{-12}}{\left(\left(y^{\frac{7}{3}}x^{7}\right)^{-2}\right)^{3}}$$

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

$$\frac{z^{-12}}{\left(y^{\frac{7}{3}}x^{7}\right)^{-6}}$$

Expand \left(y^{\frac{7}{3}}x^{7}\right)^{-6}.

$$\frac{z^{-12}}{\left(y^{\frac{7}{3}}\right)^{-6}\left(x^{7}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{3} and -6 to get -14.

$$\frac{z^{-12}}{y^{-14}\left(x^{7}\right)^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -6 to get -42.

$$\frac{z^{-12}}{y^{-14}x^{-42}}$$