Solve (frac{25x^{7}y^2z^4}{5x^2})^3

$$( \frac { 25 x ^ { 7 } y ^ { 2 } z ^ { 4 } } { 5 x ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$125y^{6}z^{12}x^{15}$$

Solution Steps

Cancel out 5x^{2} in both numerator and denominator.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$5^{3}y^{6}\left(z^{4}\right)^{3}\left(x^{5}\right)^{3}$$

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

$$5^{3}y^{6}z^{12}\left(x^{5}\right)^{3}$$

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

$$5^{3}y^{6}z^{12}x^{15}$$

Calculate 5 to the power of 3 and get 125.

$$125y^{6}z^{12}x^{15}$$

Expand

$$125y^{6}z^{12}x^{15}$$

Solution Steps

Cancel out 5x^{2} in both numerator and denominator.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$5^{3}y^{6}\left(z^{4}\right)^{3}\left(x^{5}\right)^{3}$$

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

$$5^{3}y^{6}z^{12}\left(x^{5}\right)^{3}$$

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

$$5^{3}y^{6}z^{12}x^{15}$$

Calculate 5 to the power of 3 and get 125.

$$125y^{6}z^{12}x^{15}$$