Solve (2x^2/3y^7)^4

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

Evaluate

$$\frac{16x^{8}}{81y^{28}}$$

Solution Steps

To raise \frac{2x^{2}}{3y^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{2}\right)^{4}}{\left(3y^{7}\right)^{4}}$$

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

$$\frac{2^{4}\left(x^{2}\right)^{4}}{\left(3y^{7}\right)^{4}}$$

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

$$\frac{2^{4}x^{8}}{\left(3y^{7}\right)^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16x^{8}}{\left(3y^{7}\right)^{4}}$$

Expand \left(3y^{7}\right)^{4}.

$$\frac{16x^{8}}{3^{4}\left(y^{7}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\frac{16x^{8}}{3^{4}y^{28}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{16x^{8}}{81y^{28}}$$

Expand

$$\frac{16x^{8}}{81y^{28}}$$

Solution Steps

To raise \frac{2x^{2}}{3y^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{2}\right)^{4}}{\left(3y^{7}\right)^{4}}$$

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

$$\frac{2^{4}\left(x^{2}\right)^{4}}{\left(3y^{7}\right)^{4}}$$

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

$$\frac{2^{4}x^{8}}{\left(3y^{7}\right)^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16x^{8}}{\left(3y^{7}\right)^{4}}$$

Expand \left(3y^{7}\right)^{4}.

$$\frac{16x^{8}}{3^{4}\left(y^{7}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\frac{16x^{8}}{3^{4}y^{28}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{16x^{8}}{81y^{28}}$$