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

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

Evaluate

$$\frac{y^{8}}{9x^{13}}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{x^{-9}\left(y^{4}\right)^{3}}{\left(-3x^{2}y^{2}\right)^{2}}$$

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

$$\frac{x^{-9}y^{12}}{\left(-3x^{2}y^{2}\right)^{2}}$$

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

$$\frac{x^{-9}y^{12}}{\left(-3\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{x^{-9}y^{12}}{\left(-3\right)^{2}x^{4}\left(y^{2}\right)^{2}}$$

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

$$\frac{x^{-9}y^{12}}{\left(-3\right)^{2}x^{4}y^{4}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{x^{-9}y^{12}}{9x^{4}y^{4}}$$

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

$$\frac{x^{-9}y^{8}}{9x^{4}}$$

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

$$\frac{y^{8}}{9x^{13}}$$

Expand

$$\frac{y^{8}}{9x^{13}}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{x^{-9}\left(y^{4}\right)^{3}}{\left(-3x^{2}y^{2}\right)^{2}}$$

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

$$\frac{x^{-9}y^{12}}{\left(-3x^{2}y^{2}\right)^{2}}$$

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

$$\frac{x^{-9}y^{12}}{\left(-3\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{x^{-9}y^{12}}{\left(-3\right)^{2}x^{4}\left(y^{2}\right)^{2}}$$

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

$$\frac{x^{-9}y^{12}}{\left(-3\right)^{2}x^{4}y^{4}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{x^{-9}y^{12}}{9x^{4}y^{4}}$$

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

$$\frac{x^{-9}y^{8}}{9x^{4}}$$

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

$$\frac{y^{8}}{9x^{13}}$$