Solve left(5x^3yright)^4/left(5xy^2right)^3

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

Evaluate

$$\frac{5x^{9}}{y^{2}}$$

Solution Steps

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

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

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

$$\frac{5^{4}x^{12}y^{4}}{\left(5xy^{2}\right)^{3}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625x^{12}y^{4}}{\left(5xy^{2}\right)^{3}}$$

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

$$\frac{625x^{12}y^{4}}{5^{3}x^{3}\left(y^{2}\right)^{3}}$$

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

$$\frac{625x^{12}y^{4}}{5^{3}x^{3}y^{6}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{625x^{12}y^{4}}{125x^{3}y^{6}}$$

Cancel out 125x^{3}y^{4} in both numerator and denominator.

$$\frac{5x^{9}}{y^{2}}$$

Expand

$$\frac{5x^{9}}{y^{2}}$$

Solution Steps

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

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

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

$$\frac{5^{4}x^{12}y^{4}}{\left(5xy^{2}\right)^{3}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625x^{12}y^{4}}{\left(5xy^{2}\right)^{3}}$$

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

$$\frac{625x^{12}y^{4}}{5^{3}x^{3}\left(y^{2}\right)^{3}}$$

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

$$\frac{625x^{12}y^{4}}{5^{3}x^{3}y^{6}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{625x^{12}y^{4}}{125x^{3}y^{6}}$$

Cancel out 125x^{3}y^{4} in both numerator and denominator.

$$\frac{5x^{9}}{y^{2}}$$