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

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

Evaluate

$$\frac{9x^{6}}{z}$$

Solution Steps

To raise \frac{3x^{3}y^{-1}}{z^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{y^{2}}{z^{5}} times \frac{\left(3x^{3}y^{-1}\right)^{2}}{\left(z^{-2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{y^{2}\times \left(3x^{3}y^{-1}\right)^{2}}{z^{5}z^{-4}}$$

To multiply powers of the same base, add their exponents. Add 5 and -4 to get 1.

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

Expand \left(3x^{3}y^{-1}\right)^{2}.

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

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

$$\frac{y^{2}\times 3^{2}x^{6}\left(y^{-1}\right)^{2}}{z^{1}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{y^{2}\times 3^{2}x^{6}y^{-2}}{z^{1}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{y^{2}\times 9x^{6}y^{-2}}{z^{1}}$$

Multiply y^{2} and y^{-2} to get 1.

$$\frac{9x^{6}}{z^{1}}$$

Calculate z to the power of 1 and get z.

$$\frac{9x^{6}}{z}$$

Expand

$$\frac{9x^{6}}{z}$$

Solution Steps

To raise \frac{3x^{3}y^{-1}}{z^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{y^{2}}{z^{5}} times \frac{\left(3x^{3}y^{-1}\right)^{2}}{\left(z^{-2}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{y^{2}\times \left(3x^{3}y^{-1}\right)^{2}}{z^{5}z^{-4}}$$

To multiply powers of the same base, add their exponents. Add 5 and -4 to get 1.

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

Expand \left(3x^{3}y^{-1}\right)^{2}.

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

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

$$\frac{y^{2}\times 3^{2}x^{6}\left(y^{-1}\right)^{2}}{z^{1}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{y^{2}\times 3^{2}x^{6}y^{-2}}{z^{1}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{y^{2}\times 9x^{6}y^{-2}}{z^{1}}$$

Multiply y^{2} and y^{-2} to get 1.

$$\frac{9x^{6}}{z^{1}}$$

Calculate z to the power of 1 and get z.

$$\frac{9x^{6}}{z}$$