Solve (3x^{-1/4}y^{2})^{4}*x^2y^-16/27x^-4y^-6

$$( 3 x ^ { - \frac { 1 } { 4 } } y ^ { 2 } ) ^ { 4 } \times \frac { x ^ { 2 } y ^ { - 16 } } { 27 x ^ { - 4 } y ^ { - 6 } }$$

Evaluate

$$\frac{3x^{5}}{y^{2}}$$

Solution Steps

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

$$3^{4}\left(x^{-\frac{1}{4}}\right)^{4}\left(y^{2}\right)^{4}\times \frac{x^{2}y^{-16}}{27x^{-4}y^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{4} and 4 to get -1.

$$3^{4}x^{-1}\left(y^{2}\right)^{4}\times \frac{x^{2}y^{-16}}{27x^{-4}y^{-6}}$$

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

$$3^{4}x^{-1}y^{8}\times \frac{x^{2}y^{-16}}{27x^{-4}y^{-6}}$$

Calculate 3 to the power of 4 and get 81.

$$81x^{-1}y^{8}\times \frac{x^{2}y^{-16}}{27x^{-4}y^{-6}}$$

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

$$81x^{-1}y^{8}\times \frac{y^{-16}x^{6}}{27y^{-6}}$$

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

$$81x^{-1}y^{8}\times \frac{x^{6}}{27y^{10}}$$

Express 81\times \frac{x^{6}}{27y^{10}} as a single fraction.

$$\frac{81x^{6}}{27y^{10}}x^{-1}y^{8}$$

Cancel out 27 in both numerator and denominator.

$$\frac{3x^{6}}{y^{10}}x^{-1}y^{8}$$

Express \frac{3x^{6}}{y^{10}}x^{-1} as a single fraction.

$$\frac{3x^{6}x^{-1}}{y^{10}}y^{8}$$

Express \frac{3x^{6}x^{-1}}{y^{10}}y^{8} as a single fraction.

$$\frac{3x^{6}x^{-1}y^{8}}{y^{10}}$$

Cancel out y^{8} in both numerator and denominator.

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

Express 3\times \frac{1}{x} as a single fraction.

$$\frac{\frac{3}{x}x^{6}}{y^{2}}$$

Express \frac{3}{x}x^{6} as a single fraction.

$$\frac{\frac{3x^{6}}{x}}{y^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{3x^{5}}{y^{2}}$$

Expand

$$\frac{3x^{5}}{y^{2}}$$

Solution Steps

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

$$3^{4}\left(x^{-\frac{1}{4}}\right)^{4}\left(y^{2}\right)^{4}\times \frac{x^{2}y^{-16}}{27x^{-4}y^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{4} and 4 to get -1.

$$3^{4}x^{-1}\left(y^{2}\right)^{4}\times \frac{x^{2}y^{-16}}{27x^{-4}y^{-6}}$$

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

$$3^{4}x^{-1}y^{8}\times \frac{x^{2}y^{-16}}{27x^{-4}y^{-6}}$$

Calculate 3 to the power of 4 and get 81.

$$81x^{-1}y^{8}\times \frac{x^{2}y^{-16}}{27x^{-4}y^{-6}}$$

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

$$81x^{-1}y^{8}\times \frac{y^{-16}x^{6}}{27y^{-6}}$$

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

$$81x^{-1}y^{8}\times \frac{x^{6}}{27y^{10}}$$

Express 81\times \frac{x^{6}}{27y^{10}} as a single fraction.

$$\frac{81x^{6}}{27y^{10}}x^{-1}y^{8}$$

Cancel out 27 in both numerator and denominator.

$$\frac{3x^{6}}{y^{10}}x^{-1}y^{8}$$

Express \frac{3x^{6}}{y^{10}}x^{-1} as a single fraction.

$$\frac{3x^{6}x^{-1}}{y^{10}}y^{8}$$

Express \frac{3x^{6}x^{-1}}{y^{10}}y^{8} as a single fraction.

$$\frac{3x^{6}x^{-1}y^{8}}{y^{10}}$$

Cancel out y^{8} in both numerator and denominator.

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

Express 3\times \frac{1}{x} as a single fraction.

$$\frac{\frac{3}{x}x^{6}}{y^{2}}$$

Express \frac{3}{x}x^{6} as a single fraction.

$$\frac{\frac{3x^{6}}{x}}{y^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{3x^{5}}{y^{2}}$$