Solve (2x^3y^4/3z^2)^5

$$( \frac { 2 x ^ { 3 } y ^ { 4 } } { 3 z ^ { 2 } } ) ^ { 5 }$$

Evaluate

$$\frac{32x^{15}y^{20}}{243z^{10}}$$

Solution Steps

To raise \frac{2x^{3}y^{4}}{3z^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{3}y^{4}\right)^{5}}{\left(3z^{2}\right)^{5}}$$

Expand \left(2x^{3}y^{4}\right)^{5}.

$$\frac{2^{5}\left(x^{3}\right)^{5}\left(y^{4}\right)^{5}}{\left(3z^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{2^{5}x^{15}\left(y^{4}\right)^{5}}{\left(3z^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{2^{5}x^{15}y^{20}}{\left(3z^{2}\right)^{5}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32x^{15}y^{20}}{\left(3z^{2}\right)^{5}}$$

Expand \left(3z^{2}\right)^{5}.

$$\frac{32x^{15}y^{20}}{3^{5}\left(z^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{32x^{15}y^{20}}{3^{5}z^{10}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{32x^{15}y^{20}}{243z^{10}}$$

Expand

$$\frac{32x^{15}y^{20}}{243z^{10}}$$

Solution Steps

To raise \frac{2x^{3}y^{4}}{3z^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{3}y^{4}\right)^{5}}{\left(3z^{2}\right)^{5}}$$

Expand \left(2x^{3}y^{4}\right)^{5}.

$$\frac{2^{5}\left(x^{3}\right)^{5}\left(y^{4}\right)^{5}}{\left(3z^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\frac{2^{5}x^{15}\left(y^{4}\right)^{5}}{\left(3z^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{2^{5}x^{15}y^{20}}{\left(3z^{2}\right)^{5}}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{32x^{15}y^{20}}{\left(3z^{2}\right)^{5}}$$

Expand \left(3z^{2}\right)^{5}.

$$\frac{32x^{15}y^{20}}{3^{5}\left(z^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{32x^{15}y^{20}}{3^{5}z^{10}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{32x^{15}y^{20}}{243z^{10}}$$