Solve (5x^{2}y^3)^2div25x^4y^5

$$( 5 x ^ { 2 } y ^ { 3 } ) ^ { 2 } \div 25 x ^ { 4 } y ^ { 5 }$$

Evaluate

$$x^{8}y^{11}$$

Solution Steps

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

$$\frac{5^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}}{25}x^{4}y^{5}$$

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

$$\frac{5^{2}x^{4}\left(y^{3}\right)^{2}}{25}x^{4}y^{5}$$

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

$$\frac{5^{2}x^{4}y^{6}}{25}x^{4}y^{5}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{4}y^{6}}{25}x^{4}y^{5}$$

Cancel out 25 and 25.

$$x^{4}y^{6}x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$x^{8}y^{6}y^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$x^{8}y^{11}$$

Expand

$$x^{8}y^{11}$$

Solution Steps

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

$$\frac{5^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}}{25}x^{4}y^{5}$$

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

$$\frac{5^{2}x^{4}\left(y^{3}\right)^{2}}{25}x^{4}y^{5}$$

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

$$\frac{5^{2}x^{4}y^{6}}{25}x^{4}y^{5}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{4}y^{6}}{25}x^{4}y^{5}$$

Cancel out 25 and 25.

$$x^{4}y^{6}x^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$x^{8}y^{6}y^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$x^{8}y^{11}$$