Solve (-2ay^2)^4/(a^4y)^3

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

Evaluate

$$\frac{16y^{5}}{a^{8}}$$

Solution Steps

Expand \left(-2ay^{2}\right)^{4}.

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

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

$$\frac{\left(-2\right)^{4}a^{4}y^{8}}{\left(a^{4}y\right)^{3}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{16a^{4}y^{8}}{\left(a^{4}y\right)^{3}}$$

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

$$\frac{16a^{4}y^{8}}{\left(a^{4}\right)^{3}y^{3}}$$

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

$$\frac{16a^{4}y^{8}}{a^{12}y^{3}}$$

Cancel out y^{3}a^{4} in both numerator and denominator.

$$\frac{16y^{5}}{a^{8}}$$

Expand

$$\frac{16y^{5}}{a^{8}}$$

Solution Steps

Expand \left(-2ay^{2}\right)^{4}.

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

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

$$\frac{\left(-2\right)^{4}a^{4}y^{8}}{\left(a^{4}y\right)^{3}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{16a^{4}y^{8}}{\left(a^{4}y\right)^{3}}$$

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

$$\frac{16a^{4}y^{8}}{\left(a^{4}\right)^{3}y^{3}}$$

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

$$\frac{16a^{4}y^{8}}{a^{12}y^{3}}$$

Cancel out y^{3}a^{4} in both numerator and denominator.

$$\frac{16y^{5}}{a^{8}}$$