Solve (frac{x^frac{1{2}}y^-2}{yx^-frac{7{4}}})^4

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

Evaluate

$$\frac{x^{9}}{y^{12}}$$

Solution Steps

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

$$\left(\frac{y^{-2}x^{\frac{9}{4}}}{y}\right)^{4}$$

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

$$\left(\frac{x^{\frac{9}{4}}}{y^{3}}\right)^{4}$$

To raise \frac{x^{\frac{9}{4}}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{\frac{9}{4}}\right)^{4}}{\left(y^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{9}{4} and 4 to get 9.

$$\frac{x^{9}}{\left(y^{3}\right)^{4}}$$

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

$$\frac{x^{9}}{y^{12}}$$

Expand

$$\frac{x^{9}}{y^{12}}$$

Solution Steps

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

$$\left(\frac{y^{-2}x^{\frac{9}{4}}}{y}\right)^{4}$$

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

$$\left(\frac{x^{\frac{9}{4}}}{y^{3}}\right)^{4}$$

To raise \frac{x^{\frac{9}{4}}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{\frac{9}{4}}\right)^{4}}{\left(y^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{9}{4} and 4 to get 9.

$$\frac{x^{9}}{\left(y^{3}\right)^{4}}$$

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

$$\frac{x^{9}}{y^{12}}$$