Solve (frac{4x^{4}y^{-1}}{y^3x^73^0})^-2

$$( \frac { 4 x ^ { 4 } y ^ { - 1 } } { y ^ { 3 } x ^ { 7 } 3 ^ { 0 } } ) ^ { - 2 }$$

Evaluate

$$\frac{x^{6}y^{8}}{16}$$

Solution Steps

Cancel out x^{4} in both numerator and denominator.

$$\left(\frac{4\times \frac{1}{y}}{3^{0}x^{3}y^{3}}\right)^{-2}$$

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

$$\left(\frac{4}{3^{0}x^{3}y^{4}}\right)^{-2}$$

Calculate 3 to the power of 0 and get 1.

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

To raise \frac{4}{1x^{3}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\left(1x^{3}y^{4}\right)^{-2}}$$

Expand \left(1x^{3}y^{4}\right)^{-2}.

$$\frac{\frac{1}{16}}{1^{-2}\left(x^{3}\right)^{-2}\left(y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{16}}{1^{-2}x^{-6}\left(y^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\frac{1}{16}}{1^{-2}x^{-6}y^{-8}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{\frac{1}{16}}{1x^{-6}y^{-8}}$$

Express \frac{\frac{1}{16}}{1x^{-6}y^{-8}} as a single fraction.

$$\frac{1}{16\times 1x^{-6}y^{-8}}$$

Multiply 16 and 1 to get 16.

$$\frac{1}{16x^{-6}y^{-8}}$$

Expand

$$\frac{x^{6}y^{8}}{16}$$

Solution Steps

Cancel out x^{4} in both numerator and denominator.

$$\left(\frac{4\times \frac{1}{y}}{3^{0}x^{3}y^{3}}\right)^{-2}$$

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

$$\left(\frac{4}{3^{0}x^{3}y^{4}}\right)^{-2}$$

Calculate 3 to the power of 0 and get 1.

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

To raise \frac{4}{1x^{3}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\left(1x^{3}y^{4}\right)^{-2}}$$

Expand \left(1x^{3}y^{4}\right)^{-2}.

$$\frac{\frac{1}{16}}{1^{-2}\left(x^{3}\right)^{-2}\left(y^{4}\right)^{-2}}$$

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

$$\frac{\frac{1}{16}}{1^{-2}x^{-6}\left(y^{4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{\frac{1}{16}}{1^{-2}x^{-6}y^{-8}}$$

Calculate 1 to the power of -2 and get 1.

$$\frac{\frac{1}{16}}{1x^{-6}y^{-8}}$$

Express \frac{\frac{1}{16}}{1x^{-6}y^{-8}} as a single fraction.

$$\frac{1}{16\times 1x^{-6}y^{-8}}$$

Multiply 16 and 1 to get 16.

$$\frac{1}{16x^{-6}y^{-8}}$$