Solve (5^{2}x^2y^2)^3*(5xy)^2

$$( 5 ^ { 2 } x ^ { 2 } y ^ { 2 } ) ^ { 3 } \times ( 5 x y ) ^ { 2 }$$

Evaluate

$$390625\left(xy\right)^{8}$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\left(25x^{2}y^{2}\right)^{3}\times \left(5xy\right)^{2}$$

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

$$25^{3}\left(x^{2}\right)^{3}\left(y^{2}\right)^{3}\times \left(5xy\right)^{2}$$

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

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

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

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

Calculate 25 to the power of 3 and get 15625.

$$15625x^{6}y^{6}\times \left(5xy\right)^{2}$$

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

$$15625x^{6}y^{6}\times 5^{2}x^{2}y^{2}$$

Calculate 5 to the power of 2 and get 25.

$$15625x^{6}y^{6}\times 25x^{2}y^{2}$$

Multiply 15625 and 25 to get 390625.

$$390625x^{6}y^{6}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$390625x^{8}y^{6}y^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$390625x^{8}y^{8}$$

Expand

$$390625\left(xy\right)^{8}$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\left(25x^{2}y^{2}\right)^{3}\times \left(5xy\right)^{2}$$

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

$$25^{3}\left(x^{2}\right)^{3}\left(y^{2}\right)^{3}\times \left(5xy\right)^{2}$$

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

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

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

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

Calculate 25 to the power of 3 and get 15625.

$$15625x^{6}y^{6}\times \left(5xy\right)^{2}$$

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

$$15625x^{6}y^{6}\times 5^{2}x^{2}y^{2}$$

Calculate 5 to the power of 2 and get 25.

$$15625x^{6}y^{6}\times 25x^{2}y^{2}$$

Multiply 15625 and 25 to get 390625.

$$390625x^{6}y^{6}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$390625x^{8}y^{6}y^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$390625x^{8}y^{8}$$