Solve (5x^{2}y^3)^2div(2bx^4y^4)

$$( 5 x ^ { 2 } y ^ { 3 } ) ^ { 2 } \div ( 2 b x ^ { 4 } y ^ { 4 } )$$

Evaluate

$$\frac{25y^{2}}{2b}$$

Solution Steps

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

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

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

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

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

$$\frac{5^{2}x^{4}y^{6}}{2bx^{4}y^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{4}y^{6}}{2bx^{4}y^{4}}$$

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

$$\frac{25y^{2}}{2b}$$

Expand

$$\frac{25y^{2}}{2b}$$

Solution Steps

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

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

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

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

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

$$\frac{5^{2}x^{4}y^{6}}{2bx^{4}y^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{4}y^{6}}{2bx^{4}y^{4}}$$

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

$$\frac{25y^{2}}{2b}$$