Solve (25a^{3}x^{3}y)^2div(5a^2x^2y^2)

$$( 25 a ^ { 3 } x ^ { 3 } y ) ^ { 2 } \div ( 5 a ^ { 2 } x ^ { 2 } y ^ { 2 } )$$

Evaluate

$$125\left(ax\right)^{4}$$

Solution Steps

Expand \left(25a^{3}x^{3}y\right)^{2}.

$$\frac{25^{2}\left(a^{3}\right)^{2}\left(x^{3}\right)^{2}y^{2}}{5a^{2}x^{2}y^{2}}$$

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

$$\frac{25^{2}a^{6}\left(x^{3}\right)^{2}y^{2}}{5a^{2}x^{2}y^{2}}$$

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

$$\frac{25^{2}a^{6}x^{6}y^{2}}{5a^{2}x^{2}y^{2}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{625a^{6}x^{6}y^{2}}{5a^{2}x^{2}y^{2}}$$

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

$$125a^{4}x^{4}$$

Expand

$$125\left(ax\right)^{4}$$

Solution Steps

Expand \left(25a^{3}x^{3}y\right)^{2}.

$$\frac{25^{2}\left(a^{3}\right)^{2}\left(x^{3}\right)^{2}y^{2}}{5a^{2}x^{2}y^{2}}$$

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

$$\frac{25^{2}a^{6}\left(x^{3}\right)^{2}y^{2}}{5a^{2}x^{2}y^{2}}$$

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

$$\frac{25^{2}a^{6}x^{6}y^{2}}{5a^{2}x^{2}y^{2}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{625a^{6}x^{6}y^{2}}{5a^{2}x^{2}y^{2}}$$

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

$$125a^{4}x^{4}$$